Partial Differential Equations

Hi I am stuck on a PDE boundary question, I think I have shown the equation seperates and understand what the boundarys mean but I am not sure how to show the general solution and then solve the boundary value problems. Please help:confused::confused:

Assume solution to the modified diffusion equation .

First it says show the equation seperates, I think the follwing is correct?:

substituting the solution into the equation:

so

Then it wants the general solution for X(x) and T(t)

and then assuming solve the boundary value problem:

for all

for all

and finally characterise the differenc between solutions for and

I have found a similiar problem in Boyce's elementary Diff equations book but just cant work it out!

Thanks