Solve the equation y"+y=f(t), y(0)= 0, y'(0) = 1 f(t) = { 1 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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Transcribed Image Text:Solve the equation y"+y=f(t), y(0) = 0, y'(0)=1
where f(t)=
1 0<t<π/2
0
a. y(t)=1-cost + sint-u(t-T/2)(1-sint)
b. y(t) = cost+u(t - π/2)(1-sint(t - π/2)
c. y(t)=1-sint +-u(t-1/2)(1-cos(t - π/2)
d.
y(t) = sint -cost-μ(t - π/2)(1-sin(t - π/2) + cos(t - π/2))
Oa
O b
O C
Od
π/2≤t<∞
F(s) =
1- e-(π/2)s
S
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