3.mw

There are 2 questions actually. The first as the title says is about taking the integral. I have 2 functions that were found numerically from the system of differential equations (see the file), and I need to take the integral of the expression that includes both of them. Maple gives me something like Int () = Int (), so it doesn't solve anything. Why can it be?

The second question is about varying the boundary conditions. If, for example, I have the system with the condition like R(x_0)=R_0, can I get the plot  of R(x,R_0)? In my case I need to vary conditions on R and mu (R(0)=R_0 and mu(0)=mu_0) and then get the plot of the integral in relation to R_0 and mu_0. Is it even possible?

Download 2222222222222222222.mw

> restart; 
> A[0] := 10^(-3); a := 10^5;
> sys := diff(R(theta), theta) = A[0]*exp(2*mu(theta))*sin(theta)/(2*a), R(theta) = 2*exp(-2*mu(theta))*(1-(diff(mu(theta), `$`(theta, 2)))-cot(theta)*(diff(mu(theta), theta)));
> cond := R(0) = 10^(-5), mu(0) = 118.92, (D(mu))(0) = 0;
> F := dsolve({cond, sys}, [R(theta), mu(theta)], numeric);
> with(plots);
> odeplot(F, [theta, R(theta)], 0 .. 3.14, color = black, thickness = 3, linestyle = 4)
> odeplot(F, [theta, mu(theta)], 0 .. 3.14, color = blue, thickness = 3, linestyle = 1)

After last two lines maple writes:

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

And gives me empty plots. I can't figure out where an error can be. Some things I noticed:

Maple doesn't calculate the system before and after zero. If I change the range from 0..3.14 to -10..10 or to 0.00001..0.00001, it gives me 2 errors for 1 plot.

Also if I change the condition mu(0) = 118.92 to mu(0) = 1 or mu(0) = 50 or mu(0) = 80, it works. After ~80 it gives an error. I can't imagine where could appear a division by 0 or some other mistake.