(a) Beginning with the general solution of the system x' = -2y, y' = 2x of Problem 13, calculate x² + y² to show that the trajectories are circles.

(b) Show similarly that the trajectories of the system x' = 1/2y, y' = -8x of Problem 15 are ellipses with equations of the form 16x² + y² = C².

Problems 13

x' = -2y, y' = 2x; x (0) = 1, y(0) = 0

Problems 15

x' = 1/2y, y' = -8x