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