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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 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);

 

 

 

restart;
with(plots);
with(plottools);
k := disk([0, 0], 3, color = white)

k1 := polygon([[0, 0], [3, 4], [3, 1]])
display({k, k1});
Error, (in plots:-display) expecting plot structures but received: {k1}
 

Dear people in mapleprims,

I haven't used maple for a long time.
By the way, I tried to modify a denominator part in an fractional expression, but I couldn't.

Original expression is 

a:=-(I__22-X__2)/(I__11*I__22-I__11*X__2-I__12*I__21-I__22*X__1+X__1*X__2);

#And, I want to change this to the form

b:=(X__2-I__22)/((x__1-I__11)*(X__2-I__22)-I__12*I__21);

How can I do this?

Thank you in advance.

taro yamada

 

Hi,

how to display the primitive in the form f^n/n . ith the command int, the response is always developed. ( i try different commands "factor",...without results) 

Thanks

QuestionInt.mw

This seems like a serious limitation of Maple module, unless I am missing something.

I am trying to refactor one of my module, putting some code in separate .mpl file, say B.mpl,  and then do, from the main module

   $include  "B.mpl"; 

 But Maple complain now that, since B.mpl has export in it, that I can't do that. 

But the code inside B.mpl works fine if I copy it back and paste it inside the module, in the same location where the $include  "B.mpl";  is

Here is an example. (Since I can't use $include  "B.mpl";  in worksheet, Maple does not like it, I replaced it in this example by read "B.mpl";

(btw, both the syntax  module A()   and A:=module() seem to be equivalent), the problem shows up with either form)

I also tried with ";" and witout ";" at the end of the $include , it still gives same error.

 

restart;

currentdir("....."); #set directory to where the folder is


module A()

read "B.mpl";

 export foo:=proc()
  0;
 end proc;
end module;

Where the file B.mpl is

export boo:=proc()
return 0;
end proc; 

How is one supposed to refactor long file to separate files if can't leave export on those proc's?  

If I put everything in one .mpl file, it works

module A()

#read "B.mpl";  

export boo:=proc()  #this proc was in B.mpl
return 0;
end proc; 

 export foo:=proc()
  0;
 end proc;
end module;

I did more testing, and found that this seems to be an issue in Maple 2020.2. Because I just tried the same thing in Maple 2019 and it worked there ! i.e. no error.

Any one knows what is going on? 

Maple 2020.2, Physics 884.   Windows 10.

Here is screen shot. Same code. Works OK in Maple 2019.2 but gives error in 2020.2

 

 

 

Hi,

How do I integrate with Units[Standard]?

For example:


 

restart

with(Units[Standard]):

I__RMS__T := int((18*Unit('A')+9*t*Unit('s')*Unit('A')/(.9*Unit('s')))^2, t = 0.1e-1*Unit('s') .. 10*Unit('s'))

Error, (in Units:-Standard:-+) the units `1` and `s` have incompatible dimensions

 

I__RMS__T := int((18*Unit('A')+9*t*Unit('A')/(.9*Unit('s')))^2, t = 0.1e-1*Unit('s') .. 10*Unit('s'))

Error, (in Units:-Standard:-+) the units `A` and `A/s` have incompatible dimensions

 

 

 

It doesn't seem like I can around this. Is there a way to ignore the units error and just calculate the value?
 

Download test.mw

What type of mathematics can perform the type of transformation seen in the uploaded worksheet?

Could it be done with the Maple plottools transform command?

Could it be a projective transformation using homogeneous coordinates?

Could it be a complex conformal transformation?

Transformation.mw

Hi, I would like to parallelize the double for loop. I am computing pairwise SPolynomials like so

for i from 1 to n-1 do

for j from i+1 to ndo

spol:=Spol(poly[i],poly[j], tdeg(op(vars))):

...

od:

od: 

I would like to parallelize this code, here is what I have done:

at_node:=proc(p1,p2,vars, polynomials)

spol:=SPolynomial(p1,p2,tdeg(op(vars))):

if NormalForm(spol, polynomials, tdeg(op(vars)))=0

return [1,0]:

fi:

end proc:

Grid[Setup]("local", num_nodes=4):

Grid[Set](at_node): # below is the main loop that fails

for idx from 1 to n-1 do

out:=Grid[Seq](at_node(polynomials[idx], polynomials[j], vars, polynomials) j=idx+1, n):

od:

The loop above fails due to the error when calling normal form. It seems that the at_node function accepts an incorrect input for p1, a list of polynomials instead of a single polynomial. Is there a way to parallelize double for-loop with Grid like that? I am not sure where my error is.

 

 

 

 

 

 

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