Consider the initial value problem for function y given by, y" - 3y + 2y = - 8(t-3), y(0) = 0, y' (0) = 0.
Consider the initial value problem for function y given by, y" - 3y + 2y = - 8(t-3), y(0) = 0, y' (0) = 0.
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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![Consider the initial value problem for function y given by,
y" - 3y +2 y = − 8(† — 3),
y(0) = 0,
(a) Find the Laplace Transform of the source function, F(s) = L[− 8(t − 3)].
F(s) = -e^(-3s)
(b) Find the Laplace Transform of the solution, Y(s) = L[y(t)].
Y(s) = -e^(-3s)/(s^2-3s+2)
(c) Find the solution y(t) of the initial value problem above.
y(t) =
(u(t-3)*e^(3/2(t-3))sin(1/2(t-3)))
Recall: If needed, the step function at c is denoted as u(t - c).
M
M
M
y (0) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F150cfd4c-3669-4450-81a4-0c9aa0cabd6a%2Fb34e9c64-ca4b-469d-b52c-873beaefb003%2Fpjbk9ls_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem for function y given by,
y" - 3y +2 y = − 8(† — 3),
y(0) = 0,
(a) Find the Laplace Transform of the source function, F(s) = L[− 8(t − 3)].
F(s) = -e^(-3s)
(b) Find the Laplace Transform of the solution, Y(s) = L[y(t)].
Y(s) = -e^(-3s)/(s^2-3s+2)
(c) Find the solution y(t) of the initial value problem above.
y(t) =
(u(t-3)*e^(3/2(t-3))sin(1/2(t-3)))
Recall: If needed, the step function at c is denoted as u(t - c).
M
M
M
y (0) = 0.
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