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# Solution: In each of 1 through 5, (a) verify that the given functions satisfy the

ISBN: 9781111427412 173

## Solution for problem 10.5 Chapter 10

Advanced Engineering Mathematics | 7th Edition

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Problem 10.5

In each of 1 through 5, (a) verify that the given functions satisfy the system, (b) write the system in matrix form X= AX for an appropriate A, (c) write n linearly independent n 1 matrix solutions 1, , n , for appropriate n, (d) use the determinant test of Theorem 10.2(2) to verify that these solutions are linearly independent, (e) form a fundamental matrix for the system, and (f) use the fundamental matrix to solve the initial value problemx 1 = 5x1 4x2 + 4x3, x 2 = 12x1 11x2 + 12x3, x 3(t)= 4x1 4x2 + 5x3 x1(t)= c1et + c3e3t , x2(t) = c2e2t + c3e3t , x3(t)= (c3 c1)et + c3e3t , x1(0)= 1, x2(0) = 3, x3(0) = 5 1

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