Prove that the following systems either do or do not have periodic solutions. (a) x = 3y x x³ , y = 2(x y) y³. (b) r = r(6 2r² r² cos²()) , = rcos()) , where (r,) are polar coordinates. (c) x = x(1 x 2y) , y = y(1 y 3x) , where x 0 and y 0