I have a problem with the solution of this PDE, how can I start to solve it?
$ \left(\partial_x^2 + \frac{1}{x}\partial_x + \partial_y^2 \right) F(x,y) = \frac{4\pi I}{x} \left(\frac{\sqrt{x^2+(y\pm M)^2}-2M} {\sqrt{x^2+(y\pm M)^2}+2M}\right)^{1/2}\delta(x-x_0)\delta(y-y_0) $
where $I$ and $M$ are the positive constants.