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Determine e At A = 5 10 eAt 5 5 5 -5 0-5 5 First, find X(t). Choose the correct answer below. A. X(t)= C. X(t)= Next, find At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula et = X(t)X(0) O ☐☐- 1 2 10t 10t 10t - 5t cos 5t - 5t e 10t e10t e-5t (1 + 5t)e 10t (1-5t)e 10t sin 5t 10t sin 5t (1+5t)e¹ cos 5t 10t sin 5t (1-5t)e 10t cos 5t -te10t 10t e 10t - e ¹0t 10t e C X(t) = D. X(t)= 1 2 3 4e 1 e-5t 2 - 5t - 5t - 5t - 5t - 5t 10t 5te 10t (1-5t)e 10t e10t (1-5)te 10t (1-5t)e 10t 0 - e 10t -e10t 0 10t 10t

Determine e At A = 5 10 eAt 5 5 5 -5 0-5 5 First, find X(t). Choose the correct answer below. A. X(t)= C. X(t)= Next, find At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula et = X(t)X(0) O ☐☐- 1 2 10t 10t 10t - 5t cos 5t - 5t e 10t e10t e-5t (1 + 5t)e 10t (1-5t)e 10t sin 5t 10t sin 5t (1+5t)e¹ cos 5t 10t sin 5t (1-5t)e 10t cos 5t -te10t 10t e 10t - e ¹0t 10t e C X(t) = D. X(t)= 1 2 3 4e 1 e-5t 2 - 5t - 5t - 5t - 5t - 5t 10t 5te 10t (1-5t)e 10t e10t (1-5)te 10t (1-5t)e 10t 0 - e 10t -e10t 0 10t 10t

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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Determine e At A = 5 10 A. X(t)= eAt First, find X(t). Choose the correct answer below. O c. X(t)= 0 - 5 Next, find e At = by first finding a fundamental matrix X(t) for x' = Ax and then using the formula et =) 5 5 5 -5 5 - 4 зе 3 10t e 1 4 e 10t e 1 2€ - 5t 10t cos 5t - 5t - 5t sin 5t (1 + 5t)e e 10t 10t (1 + 5t)e e10t sin 5t 10t (1 - 5t)e 10t 10t 10t sin 5t (1-5t)e' cos 5t - te cos 5t e 10t -6 10t 10t 10t e e 10t = X(t)X(0)¯ ¹. B. X(t)= D. X(t)= I 3 3 4 1 - 5t e e - 5t 5t - 5t e - 5t e - 5t e 10t 5te 10t (1-5t)e 10t e 10t (1-5)te ¹0 10t (1-5t)e 10t 0 e10t 10t - e¹ 0 -e 10t e 10t
Transcribed Image Text:Determine e At A = 5 10 A. X(t)= eAt First, find X(t). Choose the correct answer below. O c. X(t)= 0 - 5 Next, find e At = by first finding a fundamental matrix X(t) for x' = Ax and then using the formula et =) 5 5 5 -5 5 - 4 зе 3 10t e 1 4 e 10t e 1 2€ - 5t 10t cos 5t - 5t - 5t sin 5t (1 + 5t)e e 10t 10t (1 + 5t)e e10t sin 5t 10t (1 - 5t)e 10t 10t 10t sin 5t (1-5t)e' cos 5t - te cos 5t e 10t -6 10t 10t 10t e e 10t = X(t)X(0)¯ ¹. B. X(t)= D. X(t)= I 3 3 4 1 - 5t e e - 5t 5t - 5t e - 5t e - 5t e 10t 5te 10t (1-5t)e 10t e 10t (1-5)te ¹0 10t (1-5t)e 10t 0 e10t 10t - e¹ 0 -e 10t e 10t
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