1. For the following systems of differential equations, answer the following questions. (Note that the

systems are the same as in the preceding problem set, problem 3. You don't have to rework the

problems: you may use your results from above.)

(a) (3 pts)

x' = 4x + y

y' = 6x - y

i. Use the eigenvalues to classify the equilibrium at the origin.

ii. Use the eigenvectors and eigenvalues to sketch the phase plane. Sketch several representative

solution curves.

(b) (3 pts)

x = 2x+y

y' = 4x + 5y

i. Use the eigenvalues to classify the equilibrium at the origin.

ii. Use the eigenvectors and eigenvalues to sketch the phase plane. Sketch several representative

solution curves.