11.5.2.15 Fourier method
Problem:
Find the solution of the Cauchy problem for the string oscillation equation:
\[
\begin{array}{ll}
u_{t t}=25 u_{x x}, & u(x, 0)=5 \sin 3 \pi x, \\
u_{t}(x, 0)=0, & u(0, t)=u(3, t)=0 .
\end{array}
\]