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Unformatted text preview: Problem Set 3 January 25, 2002 Due February 1, 2002 ACM 95b/100b 3pm in Firestone 303 Niles A. Pierce Include grading section number 1. Find the general solutions to the following homogeneous linear systems of ODEs. Describe the behavior of the solutions as t → ∞ . a) x = 3 6 1 2 ! x b) x = 0 1 1 1 0 1 1 1 0 x 2. Find a fundamental matrix for each of the following systems of ODEs using a similarity transformation to decouple the system. a) x = 5 1 3 1 ! x b) x = 1 1 4 3 2 1 2 1 1 x 3. Use variation of parameters to solve the following nonhomogeneous initial value problems: a) x = 2 1 3 2 ! x + e t t ! , x (0) = 1 2 ! b) x = 4 2 2 1 ! x + t 1 2 t 1 + 4 ! , x (1) = 3 ! 4. Consider the system x = 2 2 2 4 2 2 6 4 8 x a) Show that the system has a triple eigenvalue r and find one solution x (1) ( t ) of the form x = ξe rt ....
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This note was uploaded on 01/08/2011 for the course ACM 95b taught by Professor Nilesa.pierce during the Winter '09 term at Caltech.
 Winter '09
 NilesA.Pierce

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