Homework 11, due December 11, 2008.

[goodwine]

Reading: chapter 14, sections 1-3.

Problem: do either one of the two problems at the end of Chapter 14 (your choice!)

[Anon]

Professor, I have two questions:

1. For part 4 of problem 14.1, do you want us to find a general solution to the linear approximation ONLY for the equilibrium point that is farthest to the right (i.e. only the general solution for part 3), OR do you want us to find a general solution for ALL 3 equilibrium points?

2. For part 5, how do we compensate for c1 and c2 without initial conditions in the general solution in order to plot the phase portrait? If there are initial conditions, could you please point them out to me? Thanks.

[goodwine]

1. For part 4 of problem 14.1, do you want us to find a general solution to the linear approximation ONLY for the equilibrium point that is farthest to the right (i.e. only the general solution for part 3), OR do you want us to find a general solution for ALL 3 equilibrium points?

Only for the one that is farthest to the right, not all three.

2. For part 5, how do we compensate for c1 and c2 without initial conditions in the general solution in order to plot the phase portrait? If there are initial conditions, could you please point them out to me? Thanks.

It should be possible to sketch the phase portrait without picking any c1 and c2 by examining the functions in the solution. If it would help you, then just pick a few sets of values for c1 and c2 and see what the solutions are then.

[tgalx]

do the methods presented in 14.1-14.3 only work for homogeneous, constant coefficient, nonlinear d.e.'s?

[goodwine]

do the methods presented in 14.1-14.3 only work for homogeneous, constant coefficient, nonlinear d.e.'s?

Yes, that's right.