Consider wave equation with the Neumann boundary condition on the left
and "weird" b.c. on the right:
\begin{align} & u_{tt}-c^2u_{xx}=0 && 0<x<l,\label{eq-4.109}\\
& u_x (0,t)=0,\label{eq-4.11}\\
& (u_x + i \alpha u_t) (l,t)=0\label{eq-4.12}
\end{align}
with $\alpha \in \mathbb{R}$.
a. Separate variables;
b. Find "weird" eigenvalue problem for ODE;
c. Solve this problem;
d. Find simple solution $u(x,t)$.
