Consider the system of equationsdx/dt = y xf(x, y), dy/dt
Chapter 9, Problem 5(choose chapter or problem)
Consider the system of equationsdx/dt = y xf(x, y), dy/dt = x yf(x, y),where f is continuous and has continuous first partial derivatives. Show that if f(x, y) > 0in some neighborhood of the origin, then the origin is an asymptotically stable criticalpoint, and that if f(x, y) < 0 in some neighborhood of the origin, then the origin is anunstable critical point.Hint: Construct a Liapunov function of the form c(x2 + y2).
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer