@Carl Love Thank you very much, that solves the variable part.

But he is still not calculating it, eval does not seem to work. Do you know how I can make it calculate it?

solve_no_variable_v2.mw

@dharr tanks for your advice.

Event without the piecewise, it doesn't seem to work.
M_V_as_function_of_hight_cc__temporary_v3.mw

I don't know what you mean with that implicitplot.

What does that Z mean?

M_V_as_function_of_hight_cc__temporary.mw
@dharr thank you for your reply.
I want y to stay a variable. I want y_ as a function of y. So I do not want to solve y.

y is always bigger than 0.

@Carl Love Thank you all for your advice, but it's all a bit to complicated. I did what I needed to do, I don't really care about how it's done.

W(x):=subs(_C1 = 0, W(x));

This works, so that is what I will use. Crazy codes like this I can't comprehend:

W__particular:= unapply(eval(rhs(sol1), indets(sol1, suffixed(_C))=~ 0), x);

@Mariusz Iwaniuk Thank you! That does work.

I do however have to add W(x):=....

W(x):=subs(_C1 = 0, W(x));

or

W(x):=eval(W(x), _C1 = 0);

Thank you very much! It is clear now how to do it.

@Preben Alsholm 

Oke, that is clear. But can I give a value for say y and then plot it 2d with x as variable?

@Carl Love Thank you for your answer!
However, it does not seem to work, could you tell me what I am doing wrong?

@Carl Love Thank you! It worked. But it does turn purple, can it be black text?