I need to apply D'Lembert's method but in this case I don't know how. How to proceed?
Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions:
$\begin{aligned} & u(x,0)=\left\{ \begin{align}...