Exercise 101

Using the d'Alembert solution solve $y_{tt} = 9y_{xx}$, $0 < x < 1$, $t > 0$, $y(0,t) = y(1, t) = 0$, $y(x,0) = \sin (2 \pi x)$, and $y_t(x,0) = \sin (3 \pi x)$.