How do I go about solving this equation?
$\frac{\partial F(r,y)}{\partial r} = Q(r,y) - P(r,y) F(r,y) - R(r,y)F(r,y)\int_0^\infty dy'S(r,y') F(r,y')$
with the initial condition that $F(r=0,y) = 0 \ \ \forall y$
The Q's, P's R's and S's are arbitrary but well defined functions.
The above OIDE was derived whilst calculating the dark matter density using the Boltzmann equation. I have looked up various methods of solving this, both analytically and numerically. The methods which I have attempted are the Laplace transform methods and Volterra method. However, the non-linear component in the last term of the RHS is proving to be a bit difficult.
Many thanks!