2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution here. a) 2y + y = 5 sin(3t), y(0) = 0. Taking Laplace transforms gives 15 2sY(s) + Y(s) 15 s² +9 ⇒Y(s) : = (s² + 9) (2s + 1) b) y" + 2y = u(t-5), y(0) = 1, y'(0) = 1. Taking Laplace transforms gives -5s -5s e e s +3 s²Y(s) - s 1+ 2(sY(s) − 1) = ⇒Y(s) = + S s(s² + 2s) s² + 2s

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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Parts A - B please
2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution here.
a) 2y + y = 5 sin(3t), y(0) = 0. Taking Laplace transforms gives
15
2sY (s) + Y(s)
15
s² +9
⇒ Y(s) :
=
(s² + 9) (2s + 1)
b) y" + 2y = u(t – 5), y(0) = 1, y'(0) = 1. Taking Laplace transforms gives
-5s
-5s
e
e
s +3
s²Y (s) s 1+ 2(sY (s) − 1) :
⇒Y(s) =
+
S
s(s² + 2s)
s² + 2s
Transcribed Image Text:2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution here. a) 2y + y = 5 sin(3t), y(0) = 0. Taking Laplace transforms gives 15 2sY (s) + Y(s) 15 s² +9 ⇒ Y(s) : = (s² + 9) (2s + 1) b) y" + 2y = u(t – 5), y(0) = 1, y'(0) = 1. Taking Laplace transforms gives -5s -5s e e s +3 s²Y (s) s 1+ 2(sY (s) − 1) : ⇒Y(s) = + S s(s² + 2s) s² + 2s
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