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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 .
(b) Find the general solution of 324
= 2 0 2 x.
Problem 3. Use the handout Determinants and New Eigenvalue Techniques to ﬁnd the general
solution of 022
= 2 0 2 x.
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 semi-stable?
21 (b) ...
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