Use separation of variables to find a series solution of
utt = c 2uxx subject to u(0, t) =
0,
ux(l, t) + u(l, t) = 0, u(x, 0) = φ(x), &
ut(x, 0) = ψ(x) over the domain 0 < x < `, t >
0. Provide an equation that identifies the eigenvalues and sketch a
graph depicting this equation. Clearly identify the
eigenfunctions