11.5.2.11 Fourier method

Problem: Solve the boundary-value problem for the inhomogeneous wave equation: \[ \begin{array}{l} u_{t t}=a^{2} u_{x x}+t^{2} x, \quad a=2, \\ u(0, x)=\frac{\partial u}{\partial t}(0, x)=u(t, 0)=u(t, l)=0 . \end{array} \]