1d diffusion equation solution for slab with non symmetric source

[Mojo]

Disclaimer: This is a homework problem

I need to analytically solve the diffusion equation for a 1d 1 group slab with width a, and source distribution Se^(-k(x+a/2))

I've gone through the math, and come up with my homogeneous and particular solution and attempted to apply the boundary conditions of the flux set to 0 at -a/2 and a/2 but my constants are functions of each other. I was thinking of solving the source for the average, and setting the neutron current at that point to 0 but I didn't think that would work. Is there any other boundary condition I can use? I read in another text (I went through about 4 texts and 7 power points to no avail) "There always exists a physically realizable solution (no critical buckling!)") (http://www.mit.edu/~lululi/school/22.211_Nuclear_Reactor_Physics_I/notes/__all__.pdf) But I am not sure how to use this condition, or if it applies to this problem. I would greatly appreciate any insight into this.

 

[Twigg]

If you haven't tried it already, I would try finding a Green's function and taking it's convolution with the source term.