2. Suppose you are solving the wave equation of= 94 = c2Au in some region R of the plane with some nice homogeneous boundary conditions and initial conditions u(T, 0) = f(2), 24 (x, 0) = g(x). You separate variables u(i, t) = U()T(t), and as usual, you get T" + c2AT = 0 and AU + AU = 0 and the boundary conditions for U. Now assume you already happen to know the eigenvalues 0 1