Question 2 The function u(x, t) is governed by the wave equation 8²u 1 82u = 8x2 c² 8t2 Subject to the following conditions having c² = 3 i. At x = 0 and x = 1, u = 0 for all t≥ 0. ii. When t=0, = 0 for 0 ≤ x ≤1 δι δι Use the method of separation of variables to establish that the solution for u(x, t). From the solution established, given a condition t = 0, u = sinx(1 + cosx) for0≤x≤1 Find the constant b and express the solution for u(x, t) in its simplest form.