MaplePrimes Questions

I'm able to export Maple documents as LaTeX, but I'm not able to execute them because I can't find the package in

{maplestd2e}

in MikTex.

How do I add this package to MikTex, and by extension, TexnicCenter?

For the Latex code of matrix B, I used the following procedure. But the last column of B is not what we're looking for in the latex code. (There is no problem in the other columns)

Download_Latexcode.mw

restart:
interface(rtablesize=20):
f:=(x,t)->x*t;
g:=(x,t)->x^2*t;
  
B:=Matrix([[x,t,"f(x,t)","g(x,t)"],
         seq(seq([i,j,f(i,j),g(i,j)],
                 j=0.125..0.875, 0.25),
             i=0.125..0.875,0.25)]):
B[1,..]:=map(p->nprintf(`#mi(%a);`,p),B[1,..]):
B[2..,4]:=map(p->nprintf(`#mn(\"%1.2e\");`,p),B[2..,4]):
 
 

Lat:=proc(M::Matrix,
          {output::{NoUserValue,identical(string)}:=':-NoUserValue'})
  local m,n,S;
  (m,n):=op(1,M);
  S:=cat(" \\begin{tabular}",
         "{|",seq("c|",i=1..op([1,2],M)),"} ",
         "\\hline ",
         seq([seq(sprintf("$%s$ & ",latex(M[i,j],':-output'=string)),j=1..n-1),
         sprintf("$%s$ \\\\ \\hline ",latex(M[i,n],':-output'=string))][],i=1..m),
         "\\end{tabular} ");
  if output=':-string' then
    return S;
  else
    printf("%s",S);
    return NULL;
  end if;
end proc:
Lat(B);

 

The input

f(x) := x^2;

n := evalf(int(f(x)^2, x = 0 .. 1));

f(x) :=  f(x)/n;

plot(f(x), x = 0 .. 1)

leads to the error

Error, (in f) too many levels of recursion
I need to reassign the function as itself divided by n that depends on the old f...

A piece of code like this is supposed to be inside a loop, so creating f_new(x):=f(x)/n doesn't solve the issue.

If it was a cpp code I'd write something like f(x)/=n for every x. How can I do it in Maple?

Thank you in advance for you answers!

with(plots, implicitplot);

eqn := (1 + ln(x))/x = 0;

plot1 := implicitplot(eqn, x = -10 .. 10, y = -10 .. 10)

 

I'm trying to plot this equation, however no lines are showing up on the graph at all. Am I doing something wrong?

The interval I set seems to be correct, double checked it in other software

Would like to export a list into a text file

when I tried , it show ... 1234 items... , can not export a whole list into text file.

[[[0,0,0,0]], [[0,0,0,0]], .....]
thousands of [[...]] elements

 

This is an issue I had for long time. Though to ask about it.

Any one who used Database[SQLite] in Maple probably know this.  I'd like to do kernelopts('assertlevel'=2): but this does not work when using Database[SQLite] as it raises assertion failed, due to the way data is read from database and converted to Maple variable.

It happens at the statement 

         variable_to_read := Database[SQLite]:-FetchAll(stmt); 

For an example, the table I have in sql, has many fields. some are strings and some are integers. Lets say I want to read field called run_it corresponding to rowid I enter. So I do this in Maple

local run_it::integer;
.....
counter :=1;

stmt := Database[SQLite]:-Prepare(conn, cat("SELECT run_it FROM PROBLEMS WHERE rowid=",convert(counter,string),";"));    

run_it := Database[SQLite]:-FetchAll(stmt); 

The assetion error happens at the second call above. 

Error, (in dsolver_test:-MAIN_STEP) assertion failed in assignment, expected integer, got Matrix(1, 1, {(1, 1) = 1}, order = C_order, attributes = [source_rtable = (Array(1..1, {(1) = 1}, order = C_order))]) 
 

Once I remove kernelopts('assertlevel'=2): everything works fine with no problems at all. So I been running my program for more than a year now without the assert set.

Since I have hundreds of  such calls, and I do not think try/catch will work here, any one knows of a way to handle this, so I can turn on assertlevel to help catch any other problems some where else in the program, and still use SQLite ?

I could make an example if needed. I would need to create new database file and so on. This will take time.

Maple 2020.2

ps. Database[SQLite] works very well and very fast. I am surprised how fast it reads the data. few thousands records, each is 25 fields, and it does it in few seconds. Good implementation.

Edit

I found that by removing all the type specification on my Maple variables, that I read the SQL data into using FetchAll(stmt);  it now works!

So I am able to now use kernelopts('assertlevel'=2):

So intead of doing  

local local run_it::integer;  and then call SQL, I just now do  local run_it; with no type.  I had to remove the type on many such variables I had.  Now no assertion error any more during the SQL calls.

This works for me for now. I should have done this long time ago, I just did not think about it before. I would have liked to keep the type here.

Edit: I see answer below that allows me to do this by changing assert level just for the call to SQL which is good solution.

 

 

 

 

In Maple 2020.2, and after I changed to interface(warnlevel=4); then once in a while, I now see this message 

                                  Warning, persistent store makes readlib obsolete

followed by name of the file and the line number. It always happen at calls to timelimit(the_time_limit,:-dsolve(....

It seems harmless so far, as I have not seen any side effect.

 

I googled and the above, and see few places where it shows up, but no clear explanation what it is and what it means. But the messages I saw at google are a little different. They look like this

               WARNING: persistent store makes one-argument readlib obsolete

While the one I get is a little different as you can see. (no one-argument in it)

I am using my own package in .mla file during running the code if this makes any difference.

Is there any place where it explains what this means and why it happens sometimes? Sorry, can't make MWE, since it seems to happen at random. But I noticed it always happens at call to dsolve when I saw it.

Maple 2020.2

Physics 884

Windows 10
 


 

[Preliminary analysis of the Question by Carl Love:

 

In the worksheet below, the OP numerically solves a BVP on an interval a..b, for several values of a parameter. Using the numeric solution procedures returned by dsolve, he wants to numerically integrate an algebraic expression (named P1 below) that uses several of the BVP's dependent variables as well as its independent variable. This integral is to be done on an interval c..d, where a < c < d < b (all inequalities strict). He's having trouble coming up with the correct syntax for this.

 

I (Carl) am confident that the dsolve calls are all syntactically correct and that they return solution procedures in the usual manner without raising any issues, numerical or otherwise. Whether the integrations will ultimately require some adjustments to dsolve's error-control options, I don't know at this point. This Question is only about syntax required to perform the integrations. Any error-control adjustments, if they're needed at all, will be handled later.

 

I (Carl) have only edited the the OP's worksheet to remove a large amount of content that is irrelevant to Answering this Question. I haven't changed any of the content; I've only deleted. Of course, I already have several ideas about what needs to be done, but up until this point I haven't acted as an Answerer but rather as a Moderator and Editor making this Question suitable for posting.

 

--Carl Love]

restart;

 

eq1:=diff(f(y), y$4)+Uhs*diff(E(y),y$3)-(diff(f(y), y$2))+(diff(theta(y), y$1))= 0:

eq2:=diff(theta(y), y$2)+(diff(f(y), y$2)+1)^2+1+diff(theta(y),y$2) = 0:

E:=y->zeta*(cosh(k/2*(h1+h2-2*y)))/(cosh(k/2*(h1-h2))):

bcs:=f(h1) = -(1/2)*(Q-1-d), f(h2) = (1/2)*(Q-1-d), (D(f))(h1) = -1, (D(f))(h2) = -1,theta(h1) = 0, theta(h2) = 1:

 

epsilon1:=0.1:d:=1:omega:=Pi/6:h1:=-(1+epsilon1*sin(2*Pi*x)):h2:=d+epsilon2*sin(2*Pi*x+omega):F:= Q-1-d:epsilon2:=0.5:x:=1:

alpha:=Pi/6:

de:=eq1,eq2,bcs:

d1 := subs(Uhs =-2, zeta=3,k=1,[de]):

param:= {Uhs =-2, zeta=3,k=1}:

P1:= eval(diff(f(y), y$3)+Uhs*diff(E(y),y$2)-(diff(f(y), y$1)+1)+(theta(y))+sin(alpha),param);

diff(diff(diff(f(y), y), y), y)-3.524364340*cosh(-.1250000000+y)-(diff(f(y), y))-1/2+theta(y)

(1)

ec:=0.5:

 

for Q from -3 to 3 by ec do
F2[Q]:=dsolve(d1, numeric,maxmesh=25500,continuation=lambda1,output=listprocedure):
P2[Q]:=subs(F2[Q],P1):  
end do:

for Q from -3 to 3 by ec do
P3[Q]:=evalf(Int(P2[Q],0..1));   
end do:

[Examination of any of the P2[Q] or P3[Q] will highlight the syntactic problem. --Carl]:

P2[-3];

proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc-3.524364340*cosh(-.1250000000+proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc-1/2+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc

(2)

P3[-3];

Int(proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc-3.524364340*cosh(-.1250000000+proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-1.*proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc-.5000000000+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc, 0. .. 1.)

(3)

 

``

Note: If I remove the cosh from P1 then everything works fine.

Download DP_sheet_0.1.mw

I'm trying to make a table of values as a data table.  The problem is that it's making more rows than loops, I'm not able to make an empty DataFrame, and that I have to add an extra row to align the values, so I need to remove a row, and change the indexes.  Any help with making data tables work properly, would be greatly appreciated.

```

newt := x -> evalf(x - f(x)/D(f)(x));

f:= x -> x^6-2; # function to analyze

rt[0] := 1.5; #x0 value


n_error[0]:=1.5-newt(1.5): #error of first estimate
     

DF := DataFrame( <x|n_error>):# create a dataframe to store estimates, and error rates
for count from 0 to 10 do; nerror[count]:=abs(x[count]-x[count-1]);    rt[count]:=x[count-1];
x[count + 1] := newt(x[count]); DF:=Append(DF,DataSeries(<rt[count]|nerror[count]>),mode=row);    
end do:

NewtonData:=DataFrame(Remove( DF, 2, mode=row)):
NewtonData


```

In the below paper 

ODEs are solved by using Matlab Software

Is it possible to solve this in Matlab software?  [I think you mean Maple!--Carl Love]

I have attached the Article

j.physa.2019.123959.pdf

I am trying to run a Groebner Basis computation below in a for loop a few times to get an average running time.

start := time[real]():
gb := Groebner[Basis](polynomials, tdeg(op(vars)), characteristic=2^29-3):
finish := time[real]() - start:

Because Maple apparently caches the result, i was wondering if there is a way to undo this caching? Or better yet, is there a built-in tool taht would do this time measurement multiple times?

I am trying use convert(46,ordinal) to generate ordinals such as 46th. However the command produces "46th". How may I remover the double quotes so that I get 46th? I've tried using parse but it often generates an error.

I have the following link with data that I want to import to Maple and plot... any ideas how I can do that? Thanks.

https://www.gw-openscience.org/GW150914data/P150914/fig1-observed-H.txt

restart;
N := 10;
h := 0.1e-1;
print(??); # input placeholder
r := 0.2e-1;
for n to 10 do xn := sin(h*n) end do;
print(`output redirected...`); # input placeholder
                         0.009999833334
                         0.01999866669
                         0.02999550020
                         0.03998933419
                         0.04997916927
                         0.05996400648
                         0.06994284734
                         0.07991469397
                         0.08987854920
                         0.09983341665


for m to 10 do ym := cos(r*m) end do;
print(`output redirected...`); # input placeholder
                          0.9998000067
                          0.9992001067
                          0.9982005399
                          0.9968017063
                          0.9950041653
                          0.9928086359
                          0.9902159962
                          0.9872272834
                          0.9838436928
                          0.9800665778
eq := sum(sin(xn)*ym^5*u(x) = y, x = 1 .. 10);
print(`output redirected...`); # input placeholder
0.09012228112 u(1) + 0.09012228112 u(2) + 0.09012228112 u(3)

   + 0.09012228112 u(4) + 0.09012228112 u(5) + 0.09012228112 u(6)

   + 0.09012228112 u(7) + 0.09012228112 u(8) + 0.09012228112 u(9)

   + 0.09012228112 u(10) = 10. y
 

I do not know what the mistake is, help to solve please

 

I have a piece of code that solves a differential equation numerically and plots the solution, but I also want to store my values for the solution so that I can later call them easily. I want to be able to save my values for xphi for all t from 0 to 11 - not necessarily with the same variable name, it could be some k(t) - so that later when I type eg k(10) Maple gives me the value of xphi at t=10. I assume the code only requires a slight modification, but still I haven't been able to find a way to do this. Here is the corresponding piece of code. Thank you in advance.

xodephi := {diff(x(t), t) = 16250.25391*(1 - (487*x(t))/168 + 4*Pi*x(t)^(3/2) + (274229*x(t)^2)/72576 - (254*Pi*x(t)^(5/2))/21 + (119.6109573 - (856*ln(16*x(t)))/105)*x(t)^3 + (30295*Pi*x(t)^(7/2))/1728 + (7.617741607 - 23.53000000*ln(x(t)))*x(t)^4 + (535.2001594 - 102.446*ln(x(t)))*x(t)^(9/2) + (413.8828821 + 323.5521650*ln(x(t)))*x(t)^5 + (1533.899179 - 390.2690000*ln(x(t)))*x(t)^(11/2) + (2082.250556 + 423.6762500*ln(x(t)) + 33.2307*ln(x(t)^2))*x(t)^6)*x(t)^5, diff(xphi(t), t) = 5078.204347*x(t)^(3/2), x(0) = 0.03369973351, xphi(0) = a}:  #xphi(10.92469316) = 0}:

sol := dsolve(xodephi, parameters=[a], numeric):

ff:=proc(A)
  sol(parameters=[A]);
  eval(xphi(t), sol(10.92469316))
end:

A:=fsolve(ff);
sol(parameters=[A]);
sol(10.92469316);

-467.1843838

 

[a = -467.1843838]

 

[t = 10.92469316, x(t) = HFloat(0.061040830524973895), xphi(t) = HFloat(1.6909911249030074e-9)]

(1)

plots:-odeplot(sol, [t,xphi(t)], t=0..11);

 

plots:-odeplot(sol, [t,x(t)], t=0..11);

 

 

 

First 348 349 350 351 352 353 354 Last Page 350 of 2308