Consider (a) Give a brief physical interpretation. What signs must α and β...

Consider

(a) Give a brief physical interpretation. What signs must α and β have to be physical?

(b) Allow ρ, α, and β to be functions of x. Show that separation of variables works only if β = cρ, where c is a constant.

(c) If β = cρ, show that the spatial equation is a Sturm–Liouville differential equation. Solve the time equation.