11.5.5.1 Mixed problems
Problem:
Solve the mixed problem:
\[
\begin{array}{l}
u_{t t}=u_{x x}+5 u+t, 00, \\
\left.u\right|_{x=0}=0,\left.u\right|_{x=\pi}=0, \\
\left.u\right|_{t=0}=\sin 4 x,\left.u_{t}\right|_{t=0}=0 .
\end{array}
\]