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
- (a) (5 points) (Paper and pencil only) Determine all critical points of the given system of equations.
- (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.
- (c) (5 points) (Mathematica only) Draw a direction field together with critical points of the nonlinear system to confirm your conclusions.