Apply the method of Lagrange multipliers to the function (x, y) = (x 2 + 1)y subject to the constraint x 2 + y 2

Apply the method of Lagrange multipliers to the function ƒ(x, y) = (x² + 1)y subject to the constraint x² + y² = 5. First show that y ≠ 0; then treat the cases x = 0 and x ≠ 0 separately.