Explanation Given: The given matrix is: X ′ ( t ) = [ 0 1 0 0 0 1 1 − 1 1 ] X ( t ) + [ 0 0 t ] , X ( 0 ) = [ 1 − 1 0 ] and, the result of problem (9) is: e A t = 1 2 [ e t + cos t − sin t 2 sin t e t − cos t − sin t e t − cos t − sin t 2 cos t e t − cos t + sin t e t − cos t + sin t − 2 sin t e t + cos t + sin t ] Formula used: The solution of initial value problem X ′ = AX + f ( t ) , X ( 0 ) = X 0

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 9.8, Problem 24E

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The solution for the given initial value problem.

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Chapter 9.8, Problem 23E

Chapter 9.8, Problem 25E

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Fundamentals of Differential Equations and Boundary Value Problems

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Solution Summary: The author explains that the solution for the given initial value problem is: lXprime

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To find:

The solution for the given initial value problem.