) Take the Laplace transform of the following initial value and solve for Y(s) = {y(t)} Y(s) = Now find the inverse transform to find y(t) = y" + ly = sin(xt), 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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) Take the Laplace transform of the following initial value and solve for Y (s) = {y(t)}
Y(s) =
Now find the inverse transform to find y(t) =
y" + ly =
sin(xt), 0<t<1
10, 1<t
Hint: write the right hand side in terms of the Heaviside function.
(Use step(t-c) for uc (t)) Note:
(s² + ²) (s² + 1)
y(0) = 0, y(0) 0
π
T² - 1
8² +1
8² +π²
Transcribed Image Text:) Take the Laplace transform of the following initial value and solve for Y (s) = {y(t)} Y(s) = Now find the inverse transform to find y(t) = y" + ly = sin(xt), 0<t<1 10, 1<t Hint: write the right hand side in terms of the Heaviside function. (Use step(t-c) for uc (t)) Note: (s² + ²) (s² + 1) y(0) = 0, y(0) 0 π T² - 1 8² +1 8² +π²
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