Question

Given the System:
dx/dt = ax + by
dy/dt = bx + cy
1. Compute the eigenvalues for this system as functions of a, b, c.
2. b = 0 . Compute the eigenvalues for this special case and determine the exact a,c-values where this system has different types of behavior.Give the formulas for the regions in which the system has these characteristics. Then draw an accurate picture of the a,c-plane indicating the regions (i.e., the points (a,c)) where the two parameter family
dx/dt = ax
dy/dt = cy

3.repeat question 2 for some other positive b value, say b = 1.
...continued...

Answer 1

4.
Describe in words and in pictures what happens to the picture in question 3 above when you take other b-values, with b larger than 0

5. Repeat question 3 for b = -1.

6. Repeat question 4 when b < 0.