@Kitonum yes that's what I'm looking for. Thanks.

What is the logic of behind the following part of your code? Could you explain more?  

[(y,s)->y,(y,s)->s,(y,s)->eval(x(t),numSol(s))*sin(y)]

In the plot, what are our parameters? s and y? x and y etc.? 

Dear @acer,

What are the good methods in order to transform (or export) the last table to latex code?

@acer and @vv 4847

thank you so much.

@acer 

Could you explain to me what is the difference between 

A:=unapply(C(2,3),t):

and 

A:=t->C(2,3):

?

When doesn't the second code run?

Adding colorbar in plots is so complicate comparing Matlab.

We wish to making it easier with MAPLE 2019.

@acer Thank you very much.

In the code which I shared,
 

# For Linear Differential equations 
vars:=seq(c[i],i=-N..N):
A,b:=LinearAlgebra[GenerateMatrix](evalf(MatrixSystem),[vars]):
c:=linsolve(A,b);


# For Nonlinear Differential equations
c:=fsolve(evalf(MatrixSystem)):

But, your code is valid for both nonlinear and linear differential equation, is it? 

@Kitonum thanks for your interest. 

I think I'm misunderstood. I made a little change in the question. Not sin(x), it must be sin(y). In 3D plot, the axis must be ( y, t, X(t)*sin(y) )

@acer thank you.
How to define zmin , zmax and verthuebar .

what is the logic behind its?

I can't write a code for similar questions. 

@acer I edited my question.

Thank you dear @tomleslie. It is almost the answer which I want.

But, how can we remove the brackets inside the matrix P ?

@Carl Love 

thanks for your reply.

I edited the code.

- I used x instead of gamma in the code.

-you are right, f is a vector.

-I removed the brackets.

-It is the ODE with variable coefficients. I edited the code. There is a still error now?  

@tomleslie
 v is velocity. So, v with dot is acceleration. I think we assume that acceleration is fixed.  If not, I think we can' t solve, too.

If they are fixed, how can we solve?

@acer I didn't see your message.

Thanks for the warnings. I will be careful.

@vv many thanks.
If you interest, you can find special example for Matrix H in this similar post.

@vv 
I try to write a code for the following recursive matrix by considering your code. 


I am stuck with the end of the code. I highlighted it with yellow.

You can find the details in the following code. 

example.mw