Question 3. Consider the system x' = y xf(x, y), y = -x yf(x,...

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Question 3. Consider the system x' = y – xf(x, y), y = -x – yf(x, y), yf(x,y), where f is continuous and has continuous first partial derivatives. Show that if f(x, y) > 0 in some neighborhood of the origin, then the origin is a stable critical point. Hint: Try a Lyapunov function of the form x? + y². Question 3. Consider the system x' = y – xf(x, y), y = -x – yf(x, y), yf(x,y), where f is continuous and has continuous first partial derivatives. Show that if f(x, y) > 0 in some neighborhood of the origin, then the origin is a stable critical point. Hint: Try a Lyapunov function of the form x? + y².