I have a partial differential equation of the following form:
\begin{align} \frac{\partial^2 u}{\partial r_1^2}+\frac{\partial^2 u}{\partial r_2^2}+\frac{1}{r_1}\frac{\partial u}{\partial r_1}+\frac{1}{r_2}\frac{\partial u}{\partial r_2}+2\left(\lambda-\frac{1}{|r_1-r_2|^3} \right)=0 \end{align}
I am attempting to find $u(r_1,\,r_2)\equiv u$. However, I can't figure out how to solve this--I don't have a PDEs book, and resources online aren't helping with a general solution. Could someone please point me in the right direction? Thank you.
EDIT: Forget to mention--$\lambda$ is $r_1$ and $r_2$ independent.
