Question 5b: Suppose f (3:) is a smooth function, dened on the whole real line. Suppose c is a constant. Show that the equation 6u2(:n, t) = 02 6u2(:c, t) 6.732 8152 satisfying the requirement that u(x,t=0) = f(x) has solution u(x,t) = .52: [f(x+ct) + f(a; ct)]