3. (20 points) Find the general form of the series solution to
$u_t + hu = ku_{xx}$ for $0 < x < l$, $t > 0$,
$u(0, t) = u(l, t) = 0$ for $t > 0$,
$u(x, 0) = u_0(x)$ for $0 < x < l$.
Hint: there are 2 ways to do the separation of variables. It is easier if you group terms
as written above, but both approaches work.