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I have this differential equation. $$Dc''+H=0 $$
where the partial of the concentration is with respect to z the distance. H is the rate per unit volume of particles generated and D is the diffusion constant. I have gone completely brain dead on it.

I tried just treating it an an ordinary ODE and using direct integration but that doesn't seem to work. I also tried using Fourier transforms of derivatives but I cant obtain the inverse Fourier transform at the end because my problem is only valid for z

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What are the variables in this situation, what are $D$, $H$ and $c$ functions of? Is this a one-dimensional system or are these quantities vectors/matrices? What boundary conditions do you know? – Gareth Mar 19 '14 at 15:11
c is the concentration and is a function of z and t distance and time,D and H are constants and yes I assumed this could be treated as a one dimensional problem. The boundary conditions are that the flux is the same at the boundary and the concentration is is continuous at the boundary. These are at z<mod(L/2). – user122444 Mar 19 '14 at 16:22
If c is a function only in z then $Dc''=-H\to Dc'=-Hz+c_1 ...$ – Sameh Shenawy Mar 19 '14 at 16:24
Can WolframAlpha help? – Gareth Mar 19 '14 at 19:52

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