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

Many thanks, Kitonum and vv, for your solutions.  I had expected pdsolve() to produce an answer in one step, but until that happens, the alternatives offered by you can be quite workable substitutes.

I have a few comments regarding your question.

1. The method of multiple scales would make sense when there is
a scale parameter, usually epsilon, in the equation or its
initial/boundary conditions.  Your equation x'' + x = 0 has
no epsilon in it, and you have not provided initial/boundary
conditions, therefore seeking a solution with epsilon is not
really meaningful.

2. In your proto-algorithm, you take
    t = T0 + e*T1 + e^2*T2
    x = e*X1(T1) + e^2*X2(T1) + e^3*X3(T1)
(here I am writing e for epsilon).

I don't think you mean that.  It's likely that you meant
    x = e*X1(T0,T1,T2) + e^2*X2(T0,T1,T2) + e^3*X3(T0,T1,T2)

3. It may be possible to do what you want through
PDEtools:-dchange(), but I haven't used that function and
I don't know how to help you use it.  If I were doing this
problem, I would do it in Maple exactly how I do it by
hand on paper, and that would not be very difficult.

In view of point #1 above, I cannot illustrate the steps,
but if you provide a more realistic problem, I may give
it a try.

To print a dot instead of an asterisk for multiplication:

@Carl Thank you very much for the detailed and clear explanation of `?[]`.

@Carl That's very nice.

Your use of the `?[]` operator is new to me.  I see that `?[]`(x,[a]) yields x[a].
How does that work and where is it documented?