Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2
Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2
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:INSTRUCTION: Please box your final answer.
Find the Laplace transform of the following:
1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0)
= -2
Transcribed Image Text:f(1) = 2¹{F(s)}
1.
1
3.
t", n=1,2,3,...
5.
√t
7.
sin (at)
9.
t sin (at)
11. sin(at)-at cos (at)
13. cos(at)-at sin(at)
15. sin (at +
(at+b)
17.
sinh(at)
at
19.
et sin (bt)
21.
eat sinh (bt)
23. teat, n=1,2,3,...
(t)= u(t-c)
25.
Heaviside Function
27. u(t)f(t-c)
ct
29. e f(t)
31. --ƒ(1)
33.
35. f'(t)
37. f(") (t)
U c
ſ'ƒ(t-1)g(t)dt
Table of Laplace Transforms
f(t) = 2¹{F(s)}
2.
eat
4.
tº,p>-1
n
6.
t¹², n=1,2, 3, ...
8.
cos(at)
10.
tcos(at)
12. sin (at) + at cos(at)
14. cos(at)+ at sin(at)
16.
cos(at+b)
18.
cosh (at)
20.
eat cos (bt)
22.
eat cosh (bt)
24. f(ct)
8 (t-c)
26.
Dirac Delta Function
28. u(t)g(t)
30. t"f(t), n=1,2,3,...
32. S f (v) dv
34. f(t+T)= f(t)
36. f"(t)
s"F(s) — s"-¹ƒ (0) — s"-² f'(0)...- sf (¹-²) (0) — ƒ(n-¹) (0)
-
F(s) = L {f(t)}
1
S
n!
Sn+1
√π
3
25²
a
s² + a²
2as
(s² + a²) ²
2a³
(s² + a² ) ²
s(s²-a²)
(s² + a²) ²
s sin (b) + acos (b)
2
2
s² + a²
a
2
s² - a²
b
(s− a)² + b²
b
(s-a)²-b²
n!
(s-a)"+¹
CS
S
e-CSF (s)
F(s-c)
00
[ F (u) du
S
F(s) G(s)
SF (s)-f(0)
F(s)=2{f(t)}
1
s-a
T(p+1)
SP+1
1.3.5... (2n-1)√
n+ ²1/₂2
2n S
S
2
s² + a²
s² - a²
(s² + a² ) ²
2as²
(s² + a²) ²
s(s² +3a²)
(s² + a²)
s cos (b)-a sin (b)
s² + a²
S
s²_a²
s-a
(s-a)² + b²
S-a
(s-a)²-b²
1
+ F(+)
C
-CS
e
e="L{g(t+c)}
(-1)" F) (s)
F(s)
S
T
frest f (1) dt
е
-ST
1-e
s²F (s)-sf (0) - f'(0)
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