# MIT 18 03 - Hour Exam III Solutions (2 pages)

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## Hour Exam III Solutions

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## Hour Exam III Solutions

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Problems/Exams

Pages:
2
School:
Massachusetts Institute of Technology
Course:
18 03 - Differential Equations
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18 03 Hour Exam III Solutions April 23 2010 1 a The miminal period is 2 b f t is even 1 cos t cos 2 t cos 3 t c xp t 2 2 2 2 2 n 2 n 4 n 4 8 n2 9 2 d There is no periodic solution when n 0 2 3 or 2 a or b 1 1 1 1 c f t u t 1 u t 1 t 1 t 1 fr t u t 1 u t 1 fs t t 1 t 1 t t 3 a v t w t u t w t u d e t e 3 t d 0 0 3 t 3t e 1 e 2 e 3t t t 1 e t e t e 0 e 3t e 3 0 3 3 3 1 1 b W s L w t s 1 s 3 s 3 s 1 2 c W s 2 so p s 12 s2 4s 3 s 1 s 3 s 4s 3 s 1 1 e s s 1 1 t u t so t 1 u t 1 s s s s 10 a b s 1 c b F s 3 By coverup a 10 1 By complex 10 2 2 s 2s 10s s s 1 9 coverup multiply through by s 1 2 9 and set s to be a root say 1 3i b 3i c 1 s 1 9 3i 3i so b 1 c 0 and F s which is the Laplace 1 3i s s 1 2 9 transform of 1 e t cos 3t 4 a 5 a 0 1 3i 1 3i 2 so X s b X s W s F s F s 2 s 4 s 10 3 s 2s2 10s 2 s2 4 MIT OpenCourseWare http ocw mit edu 18 03 Differential Equations Spring 2010 For information about citing these materials or our Terms of Use visit http ocw mit edu terms

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