D'Alembert solution of the wave equation

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 $y_t(x,0) = \sin (3 \pi x)$.

Take $y_{tt} = 4y_{xx}$, $0 < x < 1$, $t > 0$, $y(0,t) = y(1, t) = 0$, $y(x,0) = x-x^2$, and $y_t(x,0) = 0$. Using the d'Alembert solution find the solution at

1. $t=0.1$,
2. $t=\nicefrac{1}{2}$,
3. $t=1$.

You may have to split your answer up by cases.

Take $y_{tt} = 100y_{xx}$, $0 < x < 4$, $t > 0$, $y(0,t) = y(4, t) = 0$, $y(x,0) = F(x)$, and $y_t(x,0) = 0$. Suppose that $F(0)=0$, $F(1)=2$, $F(2)=3$, $F(3)=1$. Using the d'Alembert solution find

1. $y(1,1)$,
2. $y(4,3)$,
3. $y(3,9)$.