Consider the initial boundary value problem (IBVP) for the wave equation: a²u a²u 4 at2 0 0 (1) и(0, t) —D и(п, t) %3D 0, t > 0 (2) u(x,0) = 0,u¿(x, 0) = sin x ,0 < x < n (3) The series u(x, t) = E-[An cos(2nt) + B, sin(2nt)] sin(nx) satisfies the wave equation (1) and the boundary conditions (2). By using the initial conditions given in (3) determine the coefficients A, and B,, and then decide which of the following is the solution of the IBVP (1) – (3). A u(x, t) = sin 4t sin 2x В u(x,t) = cos 2t sin 2x COs u(x,t) = sin t sin x D u(x,t) = cos 2t sin x E u(x, t) = sin 2t sin x