nagle_differential_equations_ISM_Part58

nagle_differential_equations_ISM_Part58 - Exercises 9.4 6....

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Unformatted text preview: Exercises 9.4 6. " x 1 ( t ) x 2 ( t ) # = " 1- 1 0 #" x 1 ( t ) x 2 ( t ) # + " t 2 # 8. x 1 ( t ) x 2 ( t ) x 3 ( t ) = 0 1 0 0 0 1- 1 1 0 x 1 ( t ) x 2 ( t ) x 3 ( t ) + cos t 10. x 1 ( t ) = 2 x 1 ( t ) + x 2 ( t ) + te t ; x 2 ( t ) =- x 1 ( t ) + 3 x 2 ( t ) + e t 12. x 1 ( t ) = x 2 ( t ) + t + 3; x 2 ( t ) = x 3 ( t )- t + 1; x 3 ( t ) =- x 1 ( t ) + x 2 ( t ) + 2 x 3 ( t ) + 2 t 14. Linearly independent 16. Linearly dependent 18. Linearly independent 20. Yes. " 3 e- t e 4 t 2 e- t- e 4 t # ; c 1 " 3 e- t 2 e- t # + c 2 " e 4 t- e 4 t # 22. Linearly independent; fundamental matrix is e t sin t- cos t e t cos t sin t e t- sin t cos t The general solution is c 1 e t e t e t + c 2 sin t cos t- sin t + c 3 - cos t sin t cos t 24. c 1 e 3 t e 3 t + c 2 - e 3 t e 3 t + c 3 - e- 3 t- e- 3 t e- 3 t + 5 t + 1 2 t 4 t + 2 281 Chapter 9 28. X- 1 ( t ) = 1 2 e t- 1 2 e t 1 2 e- 5 t 1 2 e- 5 t ; x ( t ) = " 2 e- t + e 5 t- 2 e- t + e 5 t # 32. Choosing x = col(1 , , ,..., 0), then...
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This note was uploaded on 02/12/2011 for the course MA 221 taught by Professor Mazmani during the Spring '08 term at Stevens.

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nagle_differential_equations_ISM_Part58 - Exercises 9.4 6....

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