11.5.5.7 Mixed problems

Problem: Find the solution of the mixed problem: \[ \begin{array}{l} u_{t}=\frac{1}{25} u_{x x}+17 \sin 4 t \sin 5 x \\ u(x, 0)=5 \sin 15 x+3 \pi-2 x, u(0, t)=3 \pi, u(\pi, t)=\pi \end{array} \]