Verifying a solution of the diffusion equation

[Raj Batra]

This is my attempt at the solution. I have been told that the given function is a solution. I just need to prove it. As you can see that I am stuck. What am I doing wrong?

 

[SteamKing]

What's the definition of the ∇ operator here?

Is ∇F = F_x + F_y, where F_x = ∂F / ∂x and F_y = ∂F / ∂y?

Similarly, is ∇² supposed to be the Laplacian in cartesian coordinates?

 

[Chestermiller]

The Laplacian is supposed to be evaluated in spherical coordinates in this problem. What is the equation for the Laplacian in spherical coordinates?

Chet