What did you get for the critical point?  My calculation gives T = -45926.73299, v = 0.2514345875.

But this smells like a question coming from thermodynamics, and therefore that temperature looks a bit suspicious to me.

@rrbaldino  Did you plot the two "solutions" as I suggested?  Neither of them satisfies the initial condition dy/dt=0 at t=0 that you have asked for.  One or the other answer that you have obtained may be a solution to some problem, but certainly not to your problem.

If anything, Maple should warn that both answers are wrong.

@vv What you have here is a tour de force of recursive programming.  Awesome!

I think that you are asking how to convert ln(x)/ln(10) to log₁₀(x). So far as I can tell that's not possible—Maple automatically converts logarithms from any base to base e.

For displaying purposes you may temporarily prevent the conversion by putting the desired expression in quotations, as in 'log[10](x)'; which yields log₁₀(x). But if you refer to that result later, it will revert to natural logarithms.

@nikkarkian In mathematics, "unknown" is what is to be solved for.  In your equation, V is not "unknown" because you are not solving for it.  The unkown is q(t), so all you need is:

EulerLagrange(L, t, q(t));

There are two parts to your question.  The first part is to figure out the shape and measurements of the desired net.  The second part is to draw that in Maple.

I suggest that you do the first part.  That way you can honestly claim that you did a part of the work for your project.  Then post here a hand-drawing of the net.  Many participant will be happy to show you how to do that drawing in Maple.

@Kitonum Thank you very much for this answer.  It does exactly what I was looking for.

You are attempting to solve

The differebtial equation says that the graph of  g(y) is a straight line.  But a straight line cannot fit those boundary conditions.

There may be other issues with the rest of your equations but this is the most glaring one.

@Christopher2222 Perhaps what is needed is a try_harder flag to int, as in

int(f(x), x, try_harder);

It will help to show what you have done so far on this homework assignment.  Then I am sure people will be eager to show you how to fix/improve your work.

@sarra The cross product of any pair of orthogonal unit vectors in the top plate will be equal to N (or -N). There are infinitely many such pairs, all yielding N, therefore knowing N is not enough to determine A and B.

So I repeat: Find out where the coordinates [3.5 4.2] come from, and you will have your answer.

Carl and vv, thank you very much for your clever answers, as always.

@sarra Your mutiple posts on the subject still do not answer my question about the requirement number four.

Let me put the question in a different way.

Suppose that someone tells you that the point Lt is at the location [3.5 4.2] relative to the orthogonal vectors A and B on the top-plate. Wouldn't you ask "But what are A and B"?

Whoever told you about the coordinates [3.5 4.2], should have also supplied you with the vectors A and B, otherwise that data is meaningless.

The first three specifications translate to the following Maple statements:

P := 13 * < 0, sin(10*Pi/180), cos(10*Pi/180) >;
N := < sin(18*Pi/180), 0, cos(18*Pi/180) >;
Lb := < 7, 5, 0 >;

The fourth specificaion is incomplete because it describes Lt relative to the vectors A and B, but A and B can be any pair of orthogonal vectors in the top plate.  Need to be more specific there.

@asceduardo The attached worksheet illustrates a very pedestrian approach to a multiple scale analysis of the differential equation that you have supplied.  It is incomplete since I have not applied the initial conditions, but you may complete it yourself if you feel sufficiently motivated.

multiscale.mw