solve cauchy problem not homogeneous with fundamental solution

Question

some book or some method to solve cauchy problem not homogeneous with fundamental solution in distributions theory, ie, I want to solve

$Lu=f(x,t) $

$u(0,x)=\phi(x) $

$u_t(0,x)=\psi(x)$

with $L=\partial_{tt} - k\partial_{xx} + 2\alpha \partial_t $ and $x\in\mathbb{R}$ if I know the fundamental solution E, ie, $LE=\delta$