I have this evolution equation:

$frac{d C(mu)}{dlnmu}=(y(mu))^2C(mu)$

and I have to find a numerical solution for $C$. The complication arises because I do not know the exact for of the function $y(mu)$ but I only know its evolution equation with $mu$ which looks something like:

$frac{d y(mu)}{dlnmu}=(y(mu))^3+y(mu)(f_1(mu)+f_2(mu))$

and it is complicated to analytically integrate to have a solution for $y(mu)$. But I can numerically solve it because I know the evolution equations for $f_1$ and $f_2$ and I am able to derive a closed form for these functions.

I was wondering if there is a way I can tell Mathematica to numerically solve the first equation for C, while using the numerical result from the numerical solution for the function $y$? The whole problem is that I dont know how to get an analytic form for $y(mu)$ or at least haven’t been able till now.

Thanks a lot for any help or insight!