differential equation problems

/in /by

The following is one example of it. There are 6 questions total

Consider the following system: dx/dt = xy- 3y -4

dy/dt = y^2 -x^2

  1. (a) (5 points) (Paper and pencil only) Determine all critical points of the given system of equations.
  2. (b) (5 points) (Paper and pencil only) For each critical point, find the corresponding linear system. Find the eigenvalues of each linear system; classify each critical point as to type, and determine whether it is asymptotically stable, stable, or unstable.
  3. (c) (5 points) (Mathematica only) Draw a direction field together with critical points of the nonlinear system to confirm your conclusions.