Solve Diffusion Equation for Neutron Flux in Multiplying Sphere

[EngNewbit]

This is in the beginning of a long set of problems, and I am lost. I don't get anything like this answer. Any guidance? I have a feeling its simple but haven't done much of these.

Write down the diffusion equation for the neutron flux in a multiplying sphere of radius R containing a constant distributed source of strength Q neutrons/cm3/s. Assuming that the flux vanishes at the sphere surface and that it remains finite at the origin:
Solve the diffusion equation when k inf = 1 and show that the neutron flux is given by:
(Q/6D)(R^2 − r^2)

 

[Astronuc]

One has to write the diffusion equation (in spherical coordinates) with a constant, distributed source, and apply the boundary conditions, that the flux $$\phi$$ is finite at r = 0, and 0 at r = R.

The current should also be 0 at r = 0.