1. Construct a phase diagram for the nonlinear difference equation below and use it to test for dynamic stability and confirm your results with derivative test.

Y _t = Y ^-0.5 _t-1

2. From Chiang section 17.4 questions 3b.

3. From Chiang section 17.6 questions 2.

4. From Chiang section 18.1 questions 4a and 4c.

5. From Chiang section 19.2 questions 4b.

6. Give the system of linear autonomous differential equations below, draw a phase diagram, find the equilibrium, and check the stability of the model.

Ẋ = 2y – 6

Ẏ = 8x – 16