# Solving inhomogenous bessel equation

I have the following differential equation to be solved $\dfrac{d^2\psi}{dr^2}+\dfrac{d\psi}{rdr}+4\left(\omega^2-k_0^2-\dfrac{n^2}{r^2}\right)\psi=AJ_n^2(kr)+\dfrac{k}{r}J_n(kr)J_{n+1}(kr)-\omega k^2J_{n+1}^2(kr)$ where $A$ is a constant and $k=\sqrt{\omega^2-k_0^2}$. Can you please let me know the approach to the problem?

-