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Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X ¹(0)x, is the solution to the initial value problem x' = Ax, x(0)=xo [060 x= 101 x. 110 20 (d) x(t) = X(t)x¹(0)x= x(0) = 9e 80 4 2: -5 3e 80 X(t)= 24et -4e-t -20et 8e3t 4e³t €214e³

Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X ¹(0)x, is the solution to the initial value problem x' = Ax, x(0)=xo [060 x= 101 x. 110 20 (d) x(t) = X(t)x¹(0)x= x(0) = 9e 80 4 2: -5 3e 80 X(t)= 24et -4e-t -20et 8e3t 4e³t €214e³

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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Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X ¹(0)x, is the solution to the initial value problem x' = Ax, x(0)=xo 060 x = 1 0 1 x, 110 -31 20 (d) x(t)= X(t)x¹(0)x= x(0) = 4 2 -5 9e 36-3t 31 80 80 X(t)= 24e-t -4e-t -20e-t 21 -3e 8e³t e-214e³ e-214e³
Transcribed Image Text:Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X ¹(0)x, is the solution to the initial value problem x' = Ax, x(0)=xo 060 x = 1 0 1 x, 110 -31 20 (d) x(t)= X(t)x¹(0)x= x(0) = 4 2 -5 9e 36-3t 31 80 80 X(t)= 24e-t -4e-t -20e-t 21 -3e 8e³t e-214e³ e-214e³
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