11.5.2.10 Fourier method

Problem: Solve the boundary-value problem for the homogeneous wave equation:

\begin{array}{l} u_{t t} = a^{2} u_{x x} + t, a = 1.5 \\ u (x, 0) = \frac{\partial u}{\partial t} (0, x) = u (t, 0) = u (t, l) = 0 . \end{array}