For the wave equation, utt = c2uxx, with the following boundaryand initial conditions,
u(x, 0) = 0
ut(x, 0) = 0.1x(π − x)
u(0,t) = u(Ï€,t) = 0
(a) Solve the problem using the separation of variables.
(b) Solve the problem using D’Alembert’s solution. Hint: I wouldsuggest doing an odd expansion of ut(x,0) first; the final solutionshould be exactly like the one in (a).
