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The initial value problem y4) + 2y" + y = e2t, y(0) = y'(0) = y"(0) = y'"(0) = 0 is given. If the Laplace transform of y(t) is Y(s), first find Y(s). Then using Y(s) find the solution of the given initial value problem. 1 1 (2e2t - (10t - 2)cost - (5t + 14)sint) O A. Y(s) = (s - 2) (s2 + 1} , y(t) = - 502 1 , y(t) = (2e2t - (10t - 2)cost + (5t + 14)sint) 1 B. Y(s) (s - 2) (s² + 1} ' 50 1 50 1 O C. Y(S) = (s - 2)(s² + 1} " , y(t) = (2e2* - 14)sint) + (10t – 2)cost + (5t + 1 D. Y(s) = , y(t) = (2e2t + (10t - 2)cost - (5t + 14)sint) (s - 2) (s? + 1) 50

The initial value problem y4) + 2y" + y = e2t, y(0) = y'(0) = y"(0) = y'"(0) = 0 is given. If the Laplace transform of y(t) is Y(s), first find Y(s). Then using Y(s) find the solution of the given initial value problem. 1 1 (2e2t - (10t - 2)cost - (5t + 14)sint) O A. Y(s) = (s - 2) (s2 + 1} , y(t) = - 502 1 , y(t) = (2e2t - (10t - 2)cost + (5t + 14)sint) 1 B. Y(s) (s - 2) (s² + 1} ' 50 1 50 1 O C. Y(S) = (s - 2)(s² + 1} " , y(t) = (2e2* - 14)sint) + (10t – 2)cost + (5t + 1 D. Y(s) = , y(t) = (2e2t + (10t - 2)cost - (5t + 14)sint) (s - 2) (s? + 1) 50

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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The initial value problem y(4) + 2y" + y = e2", y(0) = y'(0) = y'"(0) =y"'(0) = 0 is given. If the Laplace transform of y(t) is Y(s), first find Y(s). Then using Y(s) find the solution of the given initial value problem. 1 1 A. Y(s) = y(t) = (2e2t - (10t - 2)cost - (5t + 14)sint) (s - 2) (s? + 1} 50 1 1 (2e2t. (10t - 2)cost + (5t + 14)sint) B. Y(S) = (s - 2) (s? + 1} - y(t) = %3! 50 1 O C. Y(S) = (s - 2) (s² + 1} , y(t) = 2e2t 50 + (10t – 2)cost + (5t + 14)sint) 1 y(t) = 50 2e2t + (10t – 2)cost - (5t + 14)sint) D. Y(s) = (s - 2) (3? + 1)
Transcribed Image Text:The initial value problem y(4) + 2y" + y = e2", y(0) = y'(0) = y'"(0) =y"'(0) = 0 is given. If the Laplace transform of y(t) is Y(s), first find Y(s). Then using Y(s) find the solution of the given initial value problem. 1 1 A. Y(s) = y(t) = (2e2t - (10t - 2)cost - (5t + 14)sint) (s - 2) (s? + 1} 50 1 1 (2e2t. (10t - 2)cost + (5t + 14)sint) B. Y(S) = (s - 2) (s? + 1} - y(t) = %3! 50 1 O C. Y(S) = (s - 2) (s² + 1} , y(t) = 2e2t 50 + (10t – 2)cost + (5t + 14)sint) 1 y(t) = 50 2e2t + (10t – 2)cost - (5t + 14)sint) D. Y(s) = (s - 2) (3? + 1)
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