Hello Maple experts;

We've talked about this subject before. odetest not verifying dsolve output. And very useful input was given:

https://www.mapleprimes.com/questions/227546-How-To-Make-Odetest-Verify-Dsolve

https://www.mapleprimes.com/questions/227638-How-To-Make-Odetest-Give-Zero-On-Its

Here, I thought to give a collection from my ode database of ode's that are solved by Maple, but odetest does not give zero, all in one place. 

I know this is a hard problem to get odetest to always verify its own solution. May be each case needs custom solution?

It would be nice if this area in Maple could be improved on more if possible (Maple is already a CAS leader in solving ODE's).

If some of the experts here like to see if they can get odetest to give zero on some of these examples, they are welcome to and will be useful to see. I only tried just simplify().

I depend on odetest to tell me if my solution is correct or not, and getting false negative makes me spend more time trying to find where my error in my solution, where there might be no error there, and it is just that odetest could not verify it.

These are all from different text books. I put the reference on each ODE where it was obtained from.

Two of these ODE can also hang or take very long time. I indicated that there so one might want to skip these two.

edit added new one, #1822, uploaded new worksheet

edit 12/23/2020

Found one more.

#3647
restart;
ode:=diff(y(x),x)=2*(x*sqrt(y(x))-1)*y(x);
ic:=y(0)=1;
sol:=dsolve([ode,ic]);
odetest(sol,ode);

The above becomes zero only for x>-1 

ps. I added this to the worksheet, but since upload now does not work, did not re upload so not to lose the display above. Will do that later when it is working.

edit 12/25/2020

Found one more.

#3607
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 19.

restart;
ode:=1/2*diff(y(x),x) = (y(x)+1)^(1/2)*cos(x);
ic:=y(Pi)=0:
sol:=dsolve([ode,ic],y(x)):
res:=odetest(sol,ode);

edit 12/26/2020

Found one more

#3613
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 26.

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
res:=odetest(sol,ode);

PDEtools:-Solve(res=0,x) assuming real;

edit 1/10/2021

Found one more

#2406
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Problem number: 406.

restart;
ode:=(x^3+1)^(2/3)*diff(y(x),x)+(y(x)^3+1)^(2/3) = 0;
sol:=dsolve(ode,y(x));

check:=simplify(odetest(sol,ode));  #tried other simplication, can't get it to zero. But sol is correct

Download examples_of_odes_that_do_not_odetest.mw

Hello! I am trying to create a DEplot for some differential equations. I have used DEplot before and it works just fine and the direction field arrows appear however with this question it is not working. I have tried restarting my system, removing some options, and still am having issues. The interface version I am working with is "Standard Worksheet Interface, Maple 2020.1, Mac OS X, July 30 2020 Build ID 1482634".  Any help would be appreciated. Thank you!

Maple program for extended Euclidean algorithm for polynomials with rational coefficients

54*x^3-54*x^2+84*x-48

-12*x^3-28*x^2+72*x-32

Hello
 

I have problem that Maple is not evaluating integral (I need equation for distance for Lissajous curve):

restart;
with(Physics);
with(LinearAlgebra);
with(IntegrationTools);

x := A*sin(a*t + d);
y := B*sin(b*t);

u := diff(x, t);
u2 := diff(y, t);
u3 := sqrt(u^2 + u2^2);

u5 := int(u3, t);

I am only getting:

Hi,

I tried to find the set of real parameters a1, a2, a3, a4 and u1, u2, u3 which make a subalgebra L an ideal of a finite real Lie algebra LieAlg. Unfortunately, the "Query" command with the "Ideal" argument returns an error message that I can't get around. What should I change in this command?

restart: 
with(DifferentialGeometry):
with(LieAlgebras):
#
DGsetup([x1,x2,x3],R3):
#
Lie_Generators := [D_x1*x1+D_x2*x2+D_x3*x3, D_x3*k^2*x1+D_x1*x3, -D_x1*x2+D_x2*x1, D_x3*k^2*x2+D_x2*x3, D_x1, D_x2, D_x3]:
#
LieAlg:=LieAlgebraData(Lie_Generators):
#
DGsetup(LieAlg):
#
L:= evalDG([e3+u2*e5-u1*e6,e2-u3*e5-k^2*u1*e7,e4-u3*e6-k^2*u2*e7,e1-u1*e5-u2*e6-u3*e7]);
Sub_Alg_L:=LieAlgebraData(L);
#
TrueFalse,Equations,Solutions,IdealList:=Query(L,{u1,u2,u3},"Ideal");
#
TrueFalse,Equations,Solutions,IdealList:=Query([DGzip([a1,a2,a3,a4], L, "plus")],{a1,a2,a3,a4,u1,u2,u3},"Ideal");

Thanks for your help.

Jaqr

Dear all

I would like to solve a fourth order PDEs, using fourier transform. 

How can I apply fourier transform to get solution of my problem

Fourier_transform.mw

Thank you 

Hi, 

Let's suppose 

f := piecewise(x < 1, x, -x)

Using 

discont(f, x)

says me x=1 is a discontinuity point.
But can I obtain that f is continuous over  these two intervals?

(-infinity, 1)
[1, +infinity)

Thanks in advance

PS: I'm sure I've seen this type of question here before, but I couldn't find them.

lign1 := S*`union`(T intersect R);
                 lign1 := S (`intersect`(R, T))

lign2 := (S union T) intersect (S union R);
       lign2 := `intersect`(`union`(R, S), `union`(S, T))

verify({lign1}, {lign2});

My textbook says the expression lign1 and lign2 should be the same, but it outputs false. I suspect it's because Maple is ignoring the parenthesis in the first expression.

I m Stucked with this step

Download Pblm2.mw

Hello. I want to solve a 2X2 system using Maple. I have written this code but I do not get expected results.

restart;
with(DEtools);
with(plottools);
with(plots);
with(Algebraic);

F := -1 - y - exp(x);
G := x^2 + y*(exp(x) - 1);

sol1 := eliminate({F, G}, {x, y});

sol1 := [{x = RootOf(-exp(_Z)^2 + _Z^2 + 1), y = -exp(RootOf(-exp(_Z)^2 + _Z^2 + 1)) - 1}, {}]

But, the solutions are x=0 and y=-2 (I have solved the system by hand).

Any help?!

Hi,how to separate the letters with commas, to put them in a set like { a,b,c,d} instead of {abcd} ?

Thanks

 CAP13CombinatoireQuestion.mw?

When I try to solve this problem above error displays

Here is the file
 

Download Main.mw

Hi,

When I do large computations in a worksheet and that I manually save it, I get a message in a pop-up window which asks me if I want to save these calculations too:

1. What is it that is really saved if I answer "YES" 
2. As I always answer "NO" how can I force MAPLE to ApplyGlobally this answer (I wasn't capable to fin it out in the Preferences>Interface menu).
3. is this preference accounted for during AutoSaving?

Always in the goal to save only the necessary informations (in a mw format, export to mpl format could of course be a solution), how can I remove all the outpouts (and more specifically all the plots) in the current worksheet?
Presently I'm doing this and, before my last  saving, I turn TF to false and rexecute all _display commands ... not very practical, I agree

restart

_display := proc(tf, graph)
if tf then print(graph) end if:
end proc;

TF := true: # or false if no plot is required

# for each plot:
p := display( something ):
_display(TF, p)

Thanks in advance

How to represent this function in maple?

h(x) is sin(x)/x

I use the product() but do not how to represent the step here like 1,3,5,7.... And also the integral term not working. Making Maple frozen

Thank you!

Dear all

I have two matrices represent ( f(x[i],y[j])  and  g(x[i],y[j]) of a  given two dimensional functions.

How can I use thoses values of matrices to compute the largest distance between the two curves.

Many thanks