I find myself working with PDE's like: $$\nabla^2f = G$$ or $$\nabla^2 f + k^2f = G$$
in spherical coordinates.
I know that the homogeneous form of these equations (Laplace's and Helmholtz) have well known solutions. However, I do not know what method I could use to solve for the particular solution in each case.
Generally, the forcing function $G$ comes the previous step of a perturbation expansion, so many times it's expressed as an infinite sum, or something similar.
Is there a general method that can help me find the particular solution to these type of problems?