(2pts) Solve the following PDE with the boundary conditions and $f(x)$ as indicated. Evaluate the final sine/cosine expansion coefficients explicitly, rather than leaving them in integral form. Also, identify the steady-state solution $u_s(x)$:
$au_{xx} - u_t = 0$, ($0 < x < 2, 0 < t < \infty$)
$u(0, t) = 25$, $u_x(2, t) = 0$, $u(x, 0) = f(x)$,
Suppose f is the piecewise constant function:
$f(x) = \begin{cases} 0, & 0 < x < 1 \\ 25, & 1 < x < 2 \end{cases}$
