Your system of PDEs is highly nonlinear and a symbolic solution is extremely unlikely.  You will need to solve the system numerically.  But for that you need to supply numerical values for s, epsilon, Pr, lambda, delta.

Even then I seriously doubt the correctness of your equations. The combination du/dt + d^2 u / dy^2 forms a very ill-behaved partial differential operator. Are you sure that the plus sign is correct?  I will feel much more comfortable if it were a minus sign.

Same goes for the theta equation.

Check your equations!

Aside:  You have been posting questions on in this forum for a couple of years now, so I suppose that by now you know how to enter equations in Maple.  It will be helpful to your readers (and you!) if you could actually do that and post your worksheet instead of writing things like  s*Pr*( d)/(dy)theta +lam... which are only subject to interpretation.

If something can be implemented in some programming language, it can also be implemented in Maple.  So the direct answer to your question is YES.

If you are looking for something more specific, then you will have to be more specific.

Making an apple is easy by rotating an ellipse about the z axis.  Adding the stem and leaf is left as an exercise :-;
 

Download apple.mw

@jalal The command R[n,phi](u) rotates the vector u about the vector n through an angle phi.  It assumes that the axis of rotation goes through the origin.  In your worksheet your axis doesn't, and that's why you are getting an unexpected result.

Here I have translated the objects in your worksheet so that the rotation axis goes through the origin, and the result is a torus, as expected:

It is not too difficult to modify the proc R so that it performs a rotation about an arbitrarily positioned axis but perhaps the extra headache is not worth the trouble.  It is easier to set things up so that the rotation axis goes through the origin.

rotate-circle-animate_2.mw

@Kitonum There is no need for implicitplot3d for the second graph.  Just plot3d will do:

9*x^2*(3-z)^2+9*y*(3+z)^4 = 16*(-z^2+9)^2;
solve(%, y);
plot3d(%, x=-8..8, z=-3..3, view=-3..3);

or better yet:

9*x^2*(3-z)^2+9*y*(3+z)^4 = 16*(-z^2+9)^2;
solve(%, y);
plot3d([x,%,z], x=-8..8, z=-3..3, view=[-8..8, -3..3, -3..3]);

@vv Thank you very much for that construction.  It certainly produces the desired result.  I don't quite see how it works since I am not familiar with the Iterator package.  I will need to look into that.

@Kitonum Thanks.  That's very good.  I had looked at combinat:-permute, but didn't make the connection.

Hello @mmcdara I can't make sense of that worksheet.  Solving a nonlinear differential equation with finite elements is not exactly trivial.  I don't see anything that resembles a solution in there.

But as I wrote earlier, plugging the equation and boundary conditions into Maple produces a solution with no effort at all.

It looks to me that you have picked up a Maple code from somewhere and are attempting to apply it to a totally unrelated problem.  What are, for instance, CreateVector() and CreateMatrix()?  Furthermore, this code applies LinearSolve() to solve the resulting discretized system but your equations are nonlinear, so that won't work.

By the way, Maple's dsolve() solves your boundary value problem readily.  Why would you want to write a finite element code to solve it?

@nm Properly rounding 1.667 to two demimal places should produce 1.67 but yours produces 1.66:

fix_number(1.667,2);
        1.66

Perhaps that can be corrected with some small adjustment?

@ i see no worksheet.  Please try it again.

Upload your existing worksheet so that people can modify it as requested.

When you reply to this message, you will see a big fat green arrow in the toolbar.  Use that to upload the worksheet.

The message that you have posted, says:

If you experience any problems during installation, please visit the Maplesoft online technical support center at http://www.maplesoft.com/support.

Go to that web page and follow any of the given links there to contact technical support.

@Earl That's nice.  I converted your "Reply" to an "Answer" since it does offer an alternative approach.

@Carl Love Thanks for the compliment.  I had expected that a procedure for rotating a curve about an arbitrary axis would be included in some Maple library but as far as I can tell, it isn't.