11.5.5.7 Mixed problems

Problem: Find the solution of the mixed problem:

\begin{array}{l} u_{t} = \frac{1}{25} u_{x x} + 17 \sin 4 t \sin 5 x \\ u (x, 0) = 5 \sin 15 x + 3 π - 2 x, u (0, t) = 3 π, u (π, t) = π \end{array}