Q3) (Impulse functions) Solve the initial value problèm. 3" + 2y +y = 26 (t) – 8(t – 2), y(0) = 0, 3/(0) = 0. %3D %3D %3D Elementary Laplace Transforms

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Q3) (Impulse functions) Solve the initial value problem.
y" + 2y +y = 28(t) – 8(t – 2), y(0) = 0,
y (0) = 0.
Elementary Laplace Transforms
Line
f(t) = L-1{F(s)}
F(s) = L{f(t)}
1
1
s >0
eat
S
a
n!
3
t?, n =positive integer
s >0
4
sin at
s >0
s2
cos at
s >0
s2 + a2'
eat sin bt
s > a
(s – a)² + b²
S – a
S-a)2
+ 62'
eat cos bt
s > a
S-a2
n!
8.
t" eat, n =positive integer
s > a
(8-a)n+1:
CS
ue(t)
f(t-c)uc(t)
oft-T)g(T)dr
8(t - c)
6.
e-cs F(s)
F(s)G(s)
10
CS
11
Cs
12
s" F(s) – s-1f(0)
f(n-1)(0)
13
7.
Transcribed Image Text:Q3) (Impulse functions) Solve the initial value problem. y" + 2y +y = 28(t) – 8(t – 2), y(0) = 0, y (0) = 0. Elementary Laplace Transforms Line f(t) = L-1{F(s)} F(s) = L{f(t)} 1 1 s >0 eat S a n! 3 t?, n =positive integer s >0 4 sin at s >0 s2 cos at s >0 s2 + a2' eat sin bt s > a (s – a)² + b² S – a S-a)2 + 62' eat cos bt s > a S-a2 n! 8. t" eat, n =positive integer s > a (8-a)n+1: CS ue(t) f(t-c)uc(t) oft-T)g(T)dr 8(t - c) 6. e-cs F(s) F(s)G(s) 10 CS 11 Cs 12 s" F(s) – s-1f(0) f(n-1)(0) 13 7.
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