Given This PDE: $$\frac{\partial^2 u}{\partial t^2} - c^2 \frac{\partial^2 u}{\partial x^2} = \epsilon e^{-t/\tau} \delta(x), \quad \tau > 0,$$ How can I find the particular solution?
The boundary conditions are: $u(x=-L,t)=u(x=L,t)=0$, where $L, c$ and $\epsilon$ are given parameters.