Find the Laplace transforms of the following functions: Subject : DIFFERENTIAL EQUATIONTopic: Laplace TransformsBelow is the Table of Laplace Transforms. 1.3.5.7.9.15.17.f(t)=2*{F(s)}19.111. sin(at) at cos(at)21.t", n=1,2,3....13. cos(at)-at sin (at)sin(at+b)sinh(at)e sin (br)√tsin(at)t sin (at)e sinh(bt)23. te, n=1,2,3,...u(t)= u(t-c)Heaviside Function25.27. u(t)f(t-c)29. eºf(t)31. f(t)33. ff(t-1)g(1) dr35. f'(t)37. f(") (t)Table of Laplace TransformsF(s) = 2{f(t)}SESTE+1as² + a²2as(s² + a²)²2a³(s² + a²)²s(s²-a²)(s² + a²)²ssin (b) + acos (b)s² + a²as²-a²(s-a)² + b²b(s-a)²-8²n!(s-a)***Se™ F (s)F(s-c)*F(u) du4.f(t)=2²¹{F(s)}atetº,p>-16. 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. e" cos(bt)22. e cosh (br)24. f(ct)8 (t-c)Dirac Delta Function26.28. u(t)g(t)30. tf(t), n=1,2,3....32. ff(v) dvF(s) G(s)SF (s)-f(0) 36. f(t)34. f(t+1)=f(t)F(s) = £{f(t)}1s-aI(p+1)1-3-5---(2n-1)√2****Ss² + a²s²-a²(s² + a²)²2as²(s² + a²)²s(s²+3a²)(s² + a²)²scos (b)-a sin (b)s² + a²S5²-a²s-a(s-a)² + b²s-a(s-a)²-b²+ F(-)-cse{g(t+c)}(-1)" F") (s)F(s)SSef (t) at1-es²F (s)-sf (0)-f'(0)s" F (s)-sf (0)-5-²ƒ' (0)-sfn-²) (0)-¹) (0) 49.-2e-2 + -e310. 16x²-5cos (x√√2)-3.x23

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Answered: -2e -2t 4 3 -3x -16x²-5cos (x√√2)…

Math

Advanced Math

-2e -2t 4 3 -3x -16x²-5cos (x√√2) -5cos(x√2) 2 3

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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Question

^{Find the Laplace transforms of the following functions:}

^{Subject : DIFFERENTIAL EQUATION
Topic: Laplace Transforms}

^{Below is the Table of Laplace Transforms.}

1.
3.
5.
7.
9.
15.
17.
f(t)=2*{F(s)}
19.
1
11. sin(at) at cos(at)
21.
t", n=1,2,3....
13. cos(at)-at sin (at)
sin(at+b)
sinh(at)
e sin (br)
√t
sin(at)
t sin (at)
e sinh(bt)
23. te, n=1,2,3,...
u(t)= u(t-c)
Heaviside Function
25.
27. u(t)f(t-c)
29. eºf(t)
31. f(t)
33. ff(t-1)g(1) dr
35. f'(t)
37. f(") (t)
Table of Laplace Transforms
F(s) = 2{f(t)}
S
ESTE
+1
a
s² + a²
2as
(s² + a²)²
2a³
(s² + a²)²
s(s²-a²)
(s² + a²)²
ssin (b) + acos (b)
s² + a²
a
s²-a²
(s-a)² + b²
b
(s-a)²-8²
n!
(s-a)***
S
e™ F (s)
F(s-c)
*F(u) du
4.
f(t)=2²¹{F(s)}
at
e
tº,p>-1
6. 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. e" cos(bt)
22. e cosh (br)
24. f(ct)
8 (t-c)
Dirac Delta Function
26.
28. u(t)g(t)
30. tf(t), n=1,2,3....
32. ff(v) dv
F(s) G(s)
SF (s)-f(0) 36. f(t)
34. f(t+1)=f(t)
F(s) = £{f(t)}
1
s-a
I(p+1)
1-3-5---(2n-1)√
2****
S
s² + a²
s²-a²
(s² + a²)²
2as²
(s² + a²)²
s(s²+3a²)
(s² + a²)²
scos (b)-a sin (b)
s² + a²
S
5²-a²
s-a
(s-a)² + b²
s-a
(s-a)²-b²
+ F(-)
-cs
e{g(t+c)}
(-1)" F") (s)
F(s)
S
Sef (t) at
1-e
s²F (s)-sf (0)-f'(0)
s" F (s)-sf (0)-5-²ƒ' (0)-sfn-²) (0)-¹) (0)

4
9.-2e-2 + -e
3
10. 16x²-5cos (x√√2)
-3.x
2
3

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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