Question 3. (24 marks) Consider the one-dimensional wave equation at2 0 0. and initial conditions u(x, 0) =x4 - 2x'+x, a,u(x, 0) = 12x sin 3xx cos 3xx (a) Solve this IBVP. (1 1 marks) (b) Show that the solution is genuine for x E [0, 1] and t 2 0. (6 marks) (c) Prove that the solution to the IBVP is unique by employing the "energy method" for an appropriate function , where the energy functional is defined by E[v] (t) : NI- (2, 0 ( x, t ) ) 2 + (2, 0( x, t) ) ? do. You will need to demonstrate that this functional is 0 for all t > 0 and then show why this implies that any solution to is unique. (7 marks)