I came across this differential equation. I'm not sure if it's research level, but I think it might be:

$$u\frac{\partial}{\partial u}\left(u\frac{\partial f}{\partial u}\right) + v\frac{\partial}{\partial v}\left(v\frac{\partial f}{\partial v}\right)=\frac{\partial^2 f}{\partial u^2} + \frac{\partial^2 f}{\partial v^2}$$

Is something like this on topic/research level?

I've been trying to find out if anyone has solved this before so that I could understand their solution but haven't found anything yet.