Two dimensional, non-homogenous heat equation

Could someone please point me in the right direction for finding an analytical solution to the following (if one exists):

$\displaystyle \frac{\partial c(x,y,t)}{\partial t}=D\nabla^{2}c(x,y,t)-f(x,y,t)$

f is probably going to be a constant function and I will probably have constant initial and boundary conditions but they're not finalised yet, I'm just looking for a gentle nudge in the right direction or for someone to tell me that it's unsolvable so that I can use a numerical method.

Thanks in advance!