Homework 11, due December 11, 2008.

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

Post by goodwine »

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.

Post by 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.
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Re: Homework 11, due December 11, 2008.

Post by goodwine »

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.

Post by tgalx »

do the methods presented in 14.1-14.3 only work for homogeneous, constant coefficient, nonlinear d.e.'s?
goodwine
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Re: Homework 11, due December 11, 2008.

Post by goodwine »

tgalx wrote:do the methods presented in 14.1-14.3 only work for homogeneous, constant coefficient, nonlinear d.e.'s?
Yes, that's right.
Bill Goodwine, 376 Fitzpatrick
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