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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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