Solve the case of a vibrating string of length L with initial conditions u(x,0) = f(x), partial u(x,0)/partial x = g(x) and boundary conditions u(0,t) = a(t) and u(L,t) = b(t). Where a(t), b(t) are...

Solve the case of a vibrating string of length L with initial conditions u(x,0) = f(x), partial u(x,0)/partial x = g(x) and boundary conditions u(0,t) = a(t) and u(L,t) = b(t). Where a(t), b(t) are functions that depend on time. (Hint: Check out Partial Differential Equations: An Introduction by Walter Strauss)