The initial value problem y" + 5y" - 8y' - 12y = -48, y(0) = 8, y'(0) = 29, y"(0) = -83 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. 8s3 + 69s2 - 25 - 48 s4 + 5s3 - 8s2 - 12s A. Y(s) = y(t) = e - 3e t + 6e - 4 8s3 + 69s2 - 25 - 48 s4+ 5s3 - 8s2 - 12s B. Y(s) = y(t) = e - 3e6+ 6e + 4 8s3 + 69s2 - 2s + 48 C. Y(s) = , y(t) = et - 3e6L + 6e + 4 s4 + 553 - 8s2 - 12s 8s3 + 69s2 - 2s + 48 s4 + 5s3 - 8s2 - 12s D. Y(s) = , y(t) = e - 3e 6 + 6e - 4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The initial value problem
y" + 5y" - 8y' - 12y = -48, y(0) = 8, y'(0) = 29, y"(0) = -83
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.
8s3 + 69s2 - 25 - 48
s4 + 5s3 - 8s2 - 12s
A. Y(s) =
y(t) = e - 3e t + 6e - 4
8s3 + 69s2 - 25 - 48
s4+ 5s3 - 8s2 - 12s
B. Y(s) =
y(t) = e - 3e6+ 6e + 4
8s3 + 69s2 - 2s + 48
C. Y(s) =
, y(t) = et - 3e6L + 6e + 4
s4+ 5s3 - 8s2 - 12s
8s3 + 69s2 - 2s + 48
+ 5s3 - 8s2 - 12s
D. Y(s) =
, y(t) = et - 3e 6 + 6e - 4
Transcribed Image Text:The initial value problem y" + 5y" - 8y' - 12y = -48, y(0) = 8, y'(0) = 29, y"(0) = -83 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. 8s3 + 69s2 - 25 - 48 s4 + 5s3 - 8s2 - 12s A. Y(s) = y(t) = e - 3e t + 6e - 4 8s3 + 69s2 - 25 - 48 s4+ 5s3 - 8s2 - 12s B. Y(s) = y(t) = e - 3e6+ 6e + 4 8s3 + 69s2 - 2s + 48 C. Y(s) = , y(t) = et - 3e6L + 6e + 4 s4+ 5s3 - 8s2 - 12s 8s3 + 69s2 - 2s + 48 + 5s3 - 8s2 - 12s D. Y(s) = , y(t) = et - 3e 6 + 6e - 4
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