Question: The origin, (0, 0), is a fixed point for the system x' = x 7y 5xy 2 , y' = 2x 4y xy 2 (1)

The origin, (0, 0), is a fixed point for the system x' = x 7y 5xy2 , y' = 2x 4y xy2

(1) Show that no function of the form V = ax2 + cy2 can serve as a Lyapunov function for the system.

(2) find a Lyapunov function of the form V = ax2 + bxy + cy2 and show that the origin is asymptotically stable.

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