Use the Laplace transform to solve the given initial-value problem. 0, 0 ≤ t < T 1, π ≤ t < 2π t≥ 2π 0, y" + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = y(t) = sin(t) + 1 + cos(t) )u(t - n) + (1 - cos (t) × )u(t - 2n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the Laplace transform to solve the given initial-value problem.
0,
1,
(0,
)u(t− x) + ( 1 − cos(t) × )u(t - 2n
y" + y = f(t), y(0) = 0, y'(0) = 1, where f(t):
=
y(t) = sin(t)
+
1 + cos(t)
0≤ t < π
π ≤ t < 2π
t≥ 2π
)
Transcribed Image Text:Use the Laplace transform to solve the given initial-value problem. 0, 1, (0, )u(t− x) + ( 1 − cos(t) × )u(t - 2n y" + y = f(t), y(0) = 0, y'(0) = 1, where f(t): = y(t) = sin(t) + 1 + cos(t) 0≤ t < π π ≤ t < 2π t≥ 2π )
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