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The initial value problem y" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 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. s3 + 8s? + 15s + 12 A. Y(S) =- s4 + 4s3 + s? - 6s · y(t) = e* - e-* - 3e2t + 2 s3 + 8s? + 15s - 12 s4+ 4s3 + s2 - 6s O B. Y(S) = - y(t) = e* - e-* - 3e + 2 s3 + 8s2 - 15s - 12 s4+ 4s3 + s2 - 6s O C. Y(S) =- y(t) = et + et. 3e-2 +2 53 + 8s2 + 15s - 12 D. Y(s) = · y(t) = et + e-* - 3e-t + 2 s + 4s3 + s2 - 6s

The initial value problem y" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 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. s3 + 8s? + 15s + 12 A. Y(S) =- s4 + 4s3 + s? - 6s · y(t) = e* - e-* - 3e2t + 2 s3 + 8s? + 15s - 12 s4+ 4s3 + s2 - 6s O B. Y(S) = - y(t) = e* - e-* - 3e + 2 s3 + 8s2 - 15s - 12 s4+ 4s3 + s2 - 6s O C. Y(S) =- y(t) = et + et. 3e-2 +2 53 + 8s2 + 15s - 12 D. Y(s) = · y(t) = et + e-* - 3e-t + 2 s + 4s3 + s2 - 6s

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" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 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. s3 + 8s? + 15s + 12 O A. Y(S) = , y(t) = et - e - 3e-2t + 2 %3D s4 + 4s3 + s2 - 6s s3 + 8s? + 15s - 12 vn - + 4s3 + s? - 6s O B. Y(S) = y(t) = et - e-3 - 3e-2t + 2 53 + 8s2 - 15s - 12 O C. Y(S) = y(t) = et + e-3 - 3e* + 2 s4+ 4s3 + s? - 6s s3 + 8s2 + 15s - 12 3 +s? - 6s D. Y(S) = y(t) = et + e - 3e- + 2 s4+4s + s
Transcribed Image Text:The initial value problem y" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 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. s3 + 8s? + 15s + 12 O A. Y(S) = , y(t) = et - e - 3e-2t + 2 %3D s4 + 4s3 + s2 - 6s s3 + 8s? + 15s - 12 vn - + 4s3 + s? - 6s O B. Y(S) = y(t) = et - e-3 - 3e-2t + 2 53 + 8s2 - 15s - 12 O C. Y(S) = y(t) = et + e-3 - 3e* + 2 s4+ 4s3 + s? - 6s s3 + 8s2 + 15s - 12 3 +s? - 6s D. Y(S) = y(t) = et + e - 3e- + 2 s4+4s + s
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