Consider the PDE given by $u_{tt}=c^2u_{xx}+f(x)$ representing a vibrating string with an external force acting on it which is independent of time but depends on position.
Show that the PDE has a time-independent solution $u=h(x)$ describing how $h$ is obtained from $f$.
Plugging $u=h(x)$ into the PDE gives \begin{align*} &0=c^2h''(x)+f(x) \\ & \implies h''(x)=-\frac{f(x)}{c^2} \end{align*}
What do I need to do from here?