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Consider the nonhomogeneous system X': Find a fundamental matrix 4(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) which is a particular solution of the nonhomogeneous system. t- [ 3et 3eSt] u (t) = O A. W(t) = 2et est 2 [3e4t 3e-St] B. (t) = 2et est 21 3et 3eSt] C. p(t) = 2et u (t) = eSt 7t. 21 3ett 3est] ;u (t) = 21 t D. 4(t) = -2et e-St 7t.

Consider the nonhomogeneous system X': Find a fundamental matrix 4(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) which is a particular solution of the nonhomogeneous system. t- [ 3et 3eSt] u (t) = O A. W(t) = 2et est 2 [3e4t 3e-St] B. (t) = 2et est 21 3et 3eSt] C. p(t) = 2et u (t) = eSt 7t. 21 3ett 3est] ;u (t) = 21 t D. 4(t) = -2et e-St 7t.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the nonhomogeneous system 2 9 2 1 X' = X+ Find a fundamental matrix 4(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) which is a particular solution of the nonhomogeneous system. -2t [ 3ett -3e-St] O A. U(t) = ;u (t) = 2e4t e-St B. Q(t) = 2e4t [3ett 3e-St] - ;u (t) = e St 7t 2 e 21 81 t- 9 -2t C. H(t) = [3e4t 3e-st] u (t) 2e4t e-st 1 e 21 9t 1 t - -3ett -3est :u (t) D. W(t) = -2e4t e-St 7t 9t 21
Transcribed Image Text:Consider the nonhomogeneous system 2 9 2 1 X' = X+ Find a fundamental matrix 4(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) which is a particular solution of the nonhomogeneous system. -2t [ 3ett -3e-St] O A. U(t) = ;u (t) = 2e4t e-St B. Q(t) = 2e4t [3ett 3e-St] - ;u (t) = e St 7t 2 e 21 81 t- 9 -2t C. H(t) = [3e4t 3e-st] u (t) 2e4t e-st 1 e 21 9t 1 t - -3ett -3est :u (t) D. W(t) = -2e4t e-St 7t 9t 21
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