11.5.5.13 Mixed problems

Problem: Find the solution of the mixed problem: \[ \begin{array}{l} u_{t}=9 u_{x x}, \quad u(x, 0)=9 \sin 3 \pi x-5+2 x, \\ u(0, t)=-5, \quad u(3, t)=1 . \end{array} \]