Deriving the equation for radial wave function

Question

I'm trying to solve Schrodinger's equation of an exciton using the separation of variables method: $\psi = RY$. Here's the equation I've already derived: $$ \frac{2\mu r^2}{\hbar^2}(E+\frac{e^2}{\epsilon r})+\frac{r^2}{R}\frac{\partial^2 R}{\partial r^2}+\frac{r}{R}\frac{\partial R}{\partial r} = -\frac{1}{Y}\frac{\partial^2Y}{\partial\theta^2} $$ Where the radial wave function is $R = R(r)$ and angular part is $Y = Y(\theta)$. Since the two sides of the equation only depend on a single variable, they are both constants. I've found the angular part is $$ Y_m(\theta) = \frac{1}{\sqrt{2\pi}}e^{im\theta} $$ I'm having trouble solving the left part to obtain the radial equation. How can I do that? Thanks!