Boundary Values & Fourier Series · Challenge problem

A string $0 \le x \le \pi$ with fixed ends obeys $u_{tt} = u_{xx}$. It starts flat, $u(x, 0) = 0$, and is struck with velocity $u_t(x, 0) = x(\pi - x)$. Find $u\!\left(\dfrac\pi4, \dfrac\pi2\right)$.