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Unformatted text preview: Solutions to Homework 9 Section 7.5 1. Solving the eigenvalue problem implies that x = c 1 bracketleftbigg 1 2 bracketrightbigg e t + c 2 bracketleftbigg 2 1 bracketrightbigg e 2 t . The two asymptotes are x 2 = 2 x 1 and x 2 = (1 / 2) x 1 found by setting c 1 and c 2 to zero respectively. For c 2 negationslash = 0, all solutions will be asymptotic to x 2 = (1 / 2) x 1 as t . For c 2 = 0, the solution approches the origin along the line x 2 = 2 x 1 . x = 3 x  2 y y = 2 x  2 y4321 1 2 3 44321 1 2 3 4 x y 2. Solving the eigenvalue problem implies that x = c 1 bracketleftbigg 1 1 bracketrightbigg e t + c 2 bracketleftbigg 2 3 bracketrightbigg e 2 t . As t all solutions will approach the origin. 16. Solving the eigenvalue problem implies that x = c 1 bracketleftbigg 1 1 bracketrightbigg e t + c 2 bracketleftbigg 1 5 bracketrightbigg e 3 t , and the initial condition implies that c 1 = c 2 = 1 / 2. As t , the solution becomes asymptotic to x 2 = 5 x 1 . 1 x = 1 x  2 y y = 3 x  4 y4321 1 2 3 44321 1 2 3 4 x y 17. Solving the eigenvalue problem implies that17....
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This note was uploaded on 03/05/2009 for the course MATH 22B taught by Professor Hunter during the Spring '08 term at UC Davis.
 Spring '08
 Hunter
 Equations

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