Diffusion in two and three dimensions. (a) Show that the diffusion equation in two dimension admits the

Question:

Diffusion in two and three dimensions.
(a) Show that the diffusion equation in two dimension admits the solution

θ2(t) = (C2/t)exp (-r2/4Dt)

and in three dimensions
(b) Evaluate the constants C2 and C3. These solutions are analogous to (14) and describe the evolution of a delta function at t = 0.