Consider the autonomous systemdx/dt = y, dy/dt = x +
Chapter 9, Problem 19(choose chapter or problem)
Consider the autonomous systemdx/dt = y, dy/dt = x + 2x3.(a) Show that the critical point (0, 0) is a saddle point.(b) Sketch the trajectories for the corresponding linear system by integrating the equationfor dy/dx. Show from the parametric form of the solution that the only trajectory on whichx 0, y 0 as t is y = x.(c) Determine the trajectories for the nonlinear system by integrating the equation fordy/dx. Sketch the trajectories for the nonlinear system that correspond to y = x andy = x for the linear system.
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