Consider the non-homogeneous wave equation $$ \begin{cases} u_{tt} &= c^2 u_{xx}+Q(x,t),~~x > 0, \\ u(x,0)&=f(x), \\ u_t(x,0)&=g(x), \\ u(0,t)&=h(t). \end{cases} $$
The question is to determine the appropriate Green's function. Nothing specific about the function $Q(x,t)$ is given. The second part of the problem is to solve for $u(x,t)$ for certain values of $Q,f$ and $g.$ Any help in getting this done is much appreciated.