
11.5.2.21 Fourier method
Problem:
Find the solution of the Cauchy problem for the string oscillation equation:
\[
\begin{array}{l}
u_{t t}=5 u_{x x}, \quad u(x, 0)=e^{-(x-1)^{2}}, \\
u_{t}(x, 0)=3 \cdot e^{-(x-1)^{2}}, \quad u(0, t)=u(2, t)=0 .
\end{array}
\]