Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y" - 7y - 18y = Y(s) = = with step at t Note: 1, 0≤t<1 0, 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Take the Laplace transform of the following initial value
problem and solve for Y(s) = L{y(t)}:
1,
y" - 7y - 18y = {
0,
-0
Y(s) =
=
with step at t
Note:
Now find the inverse transform:
y(t) = □.
(Notation: write u(t-c) for the Heaviside step function uc(t)
c.)
=
0≤t<1
1≤t
1
s(s − 9) (s + 2)
-
18
y(0) = 0, y'(0) = 0
S
22
s+2
S
99
- 9
-
Transcribed Image Text:Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: 1, y" - 7y - 18y = { 0, -0 Y(s) = = with step at t Note: Now find the inverse transform: y(t) = □. (Notation: write u(t-c) for the Heaviside step function uc(t) c.) = 0≤t<1 1≤t 1 s(s − 9) (s + 2) - 18 y(0) = 0, y'(0) = 0 S 22 s+2 S 99 - 9 -
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