Advanced Math Question
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:Express the solution of the given initial value problem in terms of a convolution integral.
y" + 8y' + 4ly = sinat, y(0) = 0, y (0) = 0
y(t)
25
-8r
e
cos(25t)sin(a(t – t)) dt
y(t)
-4r
e
sin(5t)sin(a(t – t)) dt
= -
1
-47
y(t)
e 4* sin(25t)sin(a(t – t)) dr
25
y(t)
1
-8* sin(57)cos(a(t – t)) dr
e
y(t)
-4r
e
cos(5t)cos(a(t – T)) dt
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