(4) Suppose that g(0) = g(1) = 0 and that : R R is differ- entiable at every point and y = f(x) satisfies the differential equation g(x)y'(x) + y(x) = 1 for all x [0, 1]. Prove that 1 for all x = [0, 1]. Hint: Rolle's Theorem. f(x) =