Exercise 102

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.