Consider the initial value problem, 0 if t<2 y' 2 if t> 2 with y(0) = 0. Use the Laplace Transform method to solve the initial value problem, Write the solution you found as a function defined piecewise and sketch a graph of the solut
Consider the initial value problem, 0 if t<2 y' 2 if t> 2 with y(0) = 0. Use the Laplace Transform method to solve the initial value problem, Write the solution you found as a function defined piecewise and sketch a graph of the solut
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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Please used attached laplace table and indicate which f(t) and F(s)=L[f] being used from attached table thank you
Transcribed Image Text:Consider the initial value problem,
0 if t< 2
y'
2 if t> 2
with y(0) = 0.
Use the Laplace Transform method to solve the initial value problem,
Write the solution you found as a function defined piecewise and sketch a graph of the solution
![LAPLACE TRANSFORMS
Transform of basic functions
f(t)
L[ f(t) ]
1
1
1
eat
8 - a
cos(at)
s2 + a?
a
sin(at)
82 + a?
cosh(at)
82
a2
a
sinh(at)
s2 – a?
n!
tn
gn+1
e-cs
uc(t)
8(t)
1
8(t –c)
e-cs
Uc(t) f (t – c)
e-c® F(s)
where F = L[F]
ect f(t)
F(s – c)
where F = L[f]
(f * g)(t)
L[ f] L[g]
Convolution
(f * g)(t) =
f(т) 9(t — т) dт
Transform of derivatives
L[y'(t)] = sL[y] – y(0)
L[y"(t)] = s² L[y] – sy(0) – y'(0)
L[y(")(t)] = s" L[y] – s(n-1)y(0) – s(n-2)y'(0) – y(n-1)(0)
... -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322e23eb-e8ab-4947-9574-4820ae9bfba8%2Fd9f9f9d7-3e71-4c3d-b36d-6a322e924305%2F6vyh0ew_processed.png&w=3840&q=75)
Transcribed Image Text:LAPLACE TRANSFORMS
Transform of basic functions
f(t)
L[ f(t) ]
1
1
1
eat
8 - a
cos(at)
s2 + a?
a
sin(at)
82 + a?
cosh(at)
82
a2
a
sinh(at)
s2 – a?
n!
tn
gn+1
e-cs
uc(t)
8(t)
1
8(t –c)
e-cs
Uc(t) f (t – c)
e-c® F(s)
where F = L[F]
ect f(t)
F(s – c)
where F = L[f]
(f * g)(t)
L[ f] L[g]
Convolution
(f * g)(t) =
f(т) 9(t — т) dт
Transform of derivatives
L[y'(t)] = sL[y] – y(0)
L[y"(t)] = s² L[y] – sy(0) – y'(0)
L[y(")(t)] = s" L[y] – s(n-1)y(0) – s(n-2)y'(0) – y(n-1)(0)
... -
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