5. Solve the boundary value problem
\frac{\partial^2 y}{\partial t^2} = 9 \frac{\partial^2 y}{\partial x^2} + x^2 \quad (0 < x < 4, t > 0)
y(0, t) = y(4, t) = 0 \quad (t > 0),
y(x, 0) = \frac{\partial y}{\partial t}(x, 0) = 0 \quad (0 < x < 4).
Hint: Set Y(x, t) = y(x, t) + h(x) and obtain a boundary value problem for Y(x, t). Now
choose h(x) so that this boundary value problem is a familiar form.