11.5.2.21 Fourier method

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