Your system contains parameters omega and k_r for which no numerical values are given. Do you have values for these?

Runge-Kutta or rkf45 can only be used for initial value problems (IVPs). This is a boundary value problem (BVP). Better to just let dsolve choose the method.

You have numerous syntax errors which I'll show you how to correct once you supply the values of the parameters.

@wo0olf 

Use the output of dsolve as a function:

sol1(.0001);

@hacker9130368 Going from intensity=9000000 to intensity=10000000, I do get an increase in b and a decrease in c.

With intensity=9000000:

With intensity=10000000:

If you got no difference, then you probably need to set Digits to a higher value. I used Digits:= 15.

How did you embed the animation in your post? Is it a .GIF file? It is unusual in that the animation only goes through one cycle.

@mattcanderson1 Regarding Maple's use of the GPU, see ?CUDA in the Maple help system. However, this is unlikely to be any help in this thread's situation.

@manueleleonelli 

How about this?:

lower:= x^2*y, x= 0..1, y= 0..1, grid= [10$2], filled:
upper:= x^2*y-1, x= 0..1, y= 0..1, grid= [10$2], filled:
plots:-display(
     [plot3d(lower, style= wireframe),
      plot3d(lower, style= patchnogrid),
      plottools:-translate(              
           plot3d(upper, style= patchnogrid, color= pink),
           0, 0, 1
      )],
     orientation= [130,65], axes= none,
     view= [(0..1) $ 3], transparency= 0.2
);

@acer Using a= 1/2, b= 1/2, A= 0.1, B= 0.9, I get isconvex returning false without resorting to the definition. Note that f has singularities at x=0 and x=1, so using A=0, B=1 is questionable.

The false result is wrong: the function is convex.

Using eliminate instead of solve and ignoring the parametric aspect, we get the following weird result:

eliminate({
     v*(1-a) = alpha[3], a*u*v*b = alpha[2], v*a*u*(1-b) = alpha[1],
     (1/2*(-1+a))*a*p*v = alpha[33], (-1+a)*(-1+b)*a*p*v*u = alpha[13],
     (1-a)*a*p*v*u*b = alpha[23], (1/2)*a*u*v*b*(-b*u*p+b*a*u*p+b*g-g) = alpha[22],
     -a*u*v*b*(p*u-u*p*a-g-b*u*p+b*a*u*p+b*g) = alpha[12],
     (1/2)*a*u*v*(-1+b)*(-b*u*p+b*a*u*p+b*g+p*u-u*p*a) = alpha[11]
     }, {a, b, g, p, u, v}
);

@hacker9130368 Thanks for the great help on converting help files! Ironically, there is no normal help page for HelpTools:-Database:-ConvertAll. I got it to work though. After using it, you need to close your help window and re-open it; I guess it needs that to load the new index.

@mkj256 I it's more likely that it doesn't like fractions, which is how the first column is represented, To check, multiply by 1.0.

@Markiyan Hirnyk Yes, they completely rewrote the help system for Maple 18 such that help files written for earlier versions will not work. There is a way to update the help files semi-automatically, but I do not know the details of that.

If you have an earlier version of Maple, use that to read the help files.

@mkj256 Yes, I can see the faulty plot in your worksheet, but I don't understand why it happens.

@Preben Alsholm What made you suspect that there were multiple solutions?

@Kitonum 

You accidentally added an extra parameter to the system by mixing up lowercase k and uppercase K. The ODE is third order and should require only three boundary conditions.

@taro You wrote:

I can't understand how having the property of being right-associative is helpful. But, thank you for teaching me that it does not need parentheses.

The only way that it is helpful is that it avoids the need for parentheses.

By the way, the code of A Shif Operator was from Maple9's advanced programming guide, p 17.

I have the Maple 9 Advanced Programming Guide, and I have verified that what you say is true.

I cannot understand why this sort of thing happen though it does not have any typos at least for intoroductory programming guide. I have an impression that maple's books are completely proofread.

However, I do not have Maple 9 installed and I cannot verify that the code does not work in Maple 9. Are you sure that it is Maple 9 that you are using? I'd be very surprised if there was code in a Programming Guide that didn't work in the appropriate version of Maple. Indeed, I believe that the Guides are written as Maple worksheets. You can get them in worksheet form by entering "ProgrammingGuide" in the help system.