5 (3pts). Consider the wave equation ut ur for all -0 < x 0 with the initial conditions u(x,0) = e-l and u(x,0) = 0. Using the Fourier transform, show that the wave equation has a solution of f(w)etwx cos(ut)dw, where f(u) denotes the Fourier transform of e1+1, Prove 1 the form u(x, t) 2 cos(wt) cos(wax) 1+w that this solution also satisfies u(x, t) = -dw.