@tomleslie Thank you for your work: I'll definetely look into programming in Maple now to understand your code better, didn't think it could be done this way.

@Kitonum Thank you for your answer, you suggested a very interesting solution of this problem.

@rlopez Thank you very much, I was wondering what the function eval actually does, but you explained it really clearly, now I understand it fully.

@Carl Love 

Yeah, I tried: nothing worked, unfortunately. Thank you a lot for your answers anyway!

@Carl Love 

I get what you are saying. There is a singularity when theta -> 0. Still, when mu(0) = 1 or 5 there is a normal plot for mu(theta) and a strange plot for R(theta). But the fact is that the Maple shows them, despite the limit (cot(theta)*(D(mu))(theta), theta = 0, right) is infinity. When mu(0) is more than 85, the plot isn't built and that limit is still infinity. Is it a coincidence, an error of program? If so, why, as you said, does it fail to give an error message? There shouldn't be plots in either of conditions, knowing that this limit is infinity.

@Carl Love 

But why then if I change the condition mu(0) = 118.92 to mu(0) = 50, it does work?

Also cot(0)->inf, but in ODE it is multiplied by mu'(0) which is exact 0, so the singularity simply doesn't appear.