Solve the initial value problem below using the method of Laplace transforms. + X (7) = ₁, Y (7)] = 0 1, y' y" 6y' +8y= - 6 cost-4 sint, y Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 8 66 85 85 (Type an exact answer in terms of e.) y(t) = 31 - COS (1) - 201041- - cos e4t. 17 sin (t)- + 18 5 e2t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve the initial value problem below using the method of Laplace transforms.
+ x ( ) = 1, Y ( 1 ) = 0
y'
y'' - 6y' + 8y = - 6 cost - 4 sint, y
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
8
31
66
85
85
17
(Type an exact answer in terms of e.)
y(t) =
sin (t)-
cos (t)-
e4t.
+
18
5
-e2t
Transcribed Image Text:Solve the initial value problem below using the method of Laplace transforms. + x ( ) = 1, Y ( 1 ) = 0 y' y'' - 6y' + 8y = - 6 cost - 4 sint, y Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 8 31 66 85 85 17 (Type an exact answer in terms of e.) y(t) = sin (t)- cos (t)- e4t. + 18 5 -e2t
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