## Homework 11, due December 11, 2008.

Due 4:00pm, Thursday, December 11, 2008 in Prof. Goodwine's mailbox in the AME office.
goodwine
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### Homework 11, due December 11, 2008.

Reading: chapter 14, sections 1-3.

Problem: do either one of the two problems at the end of Chapter 14 (your choice!)
Bill Goodwine, 376 Fitzpatrick
Anon

### Re: Homework 11, due December 11, 2008.

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
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:

### Re: Homework 11, due December 11, 2008.

Anon wrote: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.
Bill Goodwine, 376 Fitzpatrick
tgalx

### Re: Homework 11, due December 11, 2008.

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