Finding Green's function for diffusion equation

[Glomerular]

Homework Statement

Find the solution for:
$$({\partial{}_t}^2 -D \Delta^2)G(\vec{r},t;\vec{r}_o,t_o)=\delta(\vec{r}-\vec{r}_o)\delta(t-t_o)$$
In two dimensions.

Homework Equations

The Attempt at a Solution

Am I supposed to use bessel eqs? I'm kind of stuck in starting the problem :L

 

[Orodruin]

I suggest using Fourier and/or Laplace transforms.