Quick question, what would be the general method for solving this type of problem;

(d/dt)u - (d2/dx2)u = h(x, t)

with homogeneous BCs:

u (0, t) = 0

u (L, t) = 0,

and IC u (x, 0) = f(x)

Just not sure how to deal with the RHS h(x,t) being dependent on t as well as x, (corresponding to time-dependent heat generation I think??)

What method should be used?

Thanks,

Squiggles