m260hw6 - Differential Equations Homework Assignment 6 Due...

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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 semi-stable? (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 21-260 taught by Professor Tolle during the Spring '07 term at Carnegie Mellon.

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