Considers the wave equation for the infinite string as follow
$$ \begin{cases} u_{tt}-a^2u_{xx}=f(x,t)=0, -\infty <x<+\infty,t>0 \\ u(x,0)=u_{0}(x), -\infty<x<+\infty \\ u_{t}(x,0)=u_{1}(x),-\infty<x<+\infty \end{cases} $$
I knew the way to solve above equation. As you know, its solution is d'Alembert's formula. My question is how to solve it in case $f \not\equiv 0$. Thanks everyone !