2. Use Laplace transform to solve y" + y = 6(t – 27) cos(t) y(0) = 0, y'(0) = 1 %3D %3D
2. Use Laplace transform to solve y" + y = 6(t – 27) cos(t) y(0) = 0, y'(0) = 1 %3D %3D
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:2. Use Laplace transform to solve
y" + y = 6(t – 27) cos(t)
y(0) = 0, y'(0) = 1
%3D
%3D
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![y"+y= S(t-28) cast , yloj= 0, L'10) =1
Taking oplace transfom on bath sides;
L[ y"ty]= L[S(t- 2x) Cost)
2
> se YCS)-sy l0)- y'lo)+ Y(S) = é"
Cos 2 t
(*: L[ fH) ult-a)] = é ? f(a))
as
(s*+) Y(5) - Sx0 -) ニ
2
it.
(6+1) YIS) = e
275
(: Ca82=1)
Taking beth sides;
in verse laplace on
e
こ
y(t) =
ft) Ult-27) + sint
cshene f(t)=
sin (t2T), t> 2
tく 2オ
And ult-27) s on voit step function
sint. Ult -27) +
y (t) = sint.Ult-27)+ Sint](https://content.bartleby.com/qna-images/question/e02838e7-dc45-4607-88b3-6692c936110a/706f66b3-8f1b-4e68-a63e-39f730ff5add/bil70xh_processed.jpeg)
Transcribed Image Text:y"+y= S(t-28) cast , yloj= 0, L'10) =1
Taking oplace transfom on bath sides;
L[ y"ty]= L[S(t- 2x) Cost)
2
> se YCS)-sy l0)- y'lo)+ Y(S) = é"
Cos 2 t
(*: L[ fH) ult-a)] = é ? f(a))
as
(s*+) Y(5) - Sx0 -) ニ
2
it.
(6+1) YIS) = e
275
(: Ca82=1)
Taking beth sides;
in verse laplace on
e
こ
y(t) =
ft) Ult-27) + sint
cshene f(t)=
sin (t2T), t> 2
tく 2オ
And ult-27) s on voit step function
sint. Ult -27) +
y (t) = sint.Ult-27)+ Sint
Solution
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