11.5.5.8 Mixed problems

Problem: Find the solution of the mixed problem: \[ \begin{array}{l} u_{t t}=16 u_{x x}, u(0, t)=-4, u(1, t)=-1, \\ u(x, 0)=5 \sin 2 \pi x-4+3 x, \quad u_{t}(x, 0)=0 . \end{array} \]