Consider the following problem on the interval [0, 2]: 8u(:c,t) 3m (0,25) u(2, t) : sin(3t). The next three questions will take you through writing 'u,(m, t) = 'U(m, t) l w(:r:, t) where 11(53, t) satises the boundary conditions and 111(33, t) can be found as the D'Alembert solution of a problem with homogeneous boundary conditions. You will nd 0(33, :5) explicitly and formulate the problem for w(:1:, t). Which is a good choice for v(x, t)? O None of these O v(x, t) = xe t + sin 3t O v(x, t) = (x - 2)e t + sin 3t Ov(a, t) = (x -2)et+ " sin 3t Obert + x sin 3t Ov(a, t) = et+ x- 2) sin 3t\fWith this solution method, function v(x, t) always satisfies the same initial conditions as u(x, t). O True O False