### Section 8.8

Problems 4 - 8

For problem #4, you'll need to modify the two codes from the web-page so that you have the right stopping criterion. Make sure to hand in copies of your modified code.
For problem #7, use the zero vector as your first guess.

### Section 9.1

Problems 2b, 3b, 6

For the following problem, assume that y(x) is a real-valued function.

A) For y' = a y, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points. How does your answer depend on the constant a?
B) For y' = y^2, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points.
C) For y' = -y^2, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points.
D) For y' = y^3, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points.
E) For y' = -y^3, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points.
F) For y' = a + y^2, find all the fixed points of the ODE. Find whether points initially near the fixed points move toward the fixed point or away from the fixed points. How does your answer depend on the constant a?