10. Muestre que una solución del problema de valores en la frontera
$\frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} + u$, $0 < x < \pi$, $t > 0$
$u(0, t) = 0$, $u(\pi, t) = 0$, $t > 0$
$u(x, 0) = \begin{cases} x, & 0 < x < \frac{\pi}{2} \\ \pi - x, & \frac{\pi}{2} \le x < \pi \end{cases}$
$\frac{\partial u}{\partial t}|_{t=0} = 0$, $0 < x < \pi$
$u(x, t) = \frac{4}{\pi} \sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{(2k - 1)^2} \text{sen} (2k - 1)x \cos \sqrt{(2k - 1)^2 + 1}t.$
