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Unformatted text preview: Diﬀerential Equations
Homework Assignment 6
Due on Thursday, March 3, at the start of the recitation you are registered in
Your homework should have a cover sheet with the following information: course title,
recitation, last and ﬁrst name (as they appear in the roster), number of homework. If you
use several sheets, please staple them. The problems should be written neatly and in the
order they were assigned.
Problem 1. Read the handout Determinants and New Eigenvalue Techniques posted in the Blackboard system.
Problem 2. (a) Find the eigenvectors of the matrix 324
A = 2 0 2 .
423
Show work.
(b) Find the general solution of 324
dx ¯
= 2 0 2 x.
¯
dt
423
Problem 3. Use the handout Determinants and New Eigenvalue Techniques to ﬁnd the general
solution of 022
dx ¯
= 2 0 2 x.
¯
dt
220
Problem 4. Find the general solution of the system below. Draw the phase portrait of the system.
What is the origin called in this case? Is the origin stable, unstable or semistable?
(a)
dx
¯
=
dt 12
x.
¯
03 dx
¯
=
dt 12
x.
¯
21 (b) ...
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This note was uploaded on 09/08/2011 for the course MATH 21260 taught by Professor Tolle during the Spring '07 term at Carnegie Mellon.
 Spring '07
 Tolle
 Differential Equations, Equations

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