TABLE 6.2.1 Elementary Laplace TransformsFis) = LIS))Notes1. 1s>0Sec. 6.1; Ex. 42. eSec. 6.1; Ex. 5n!3. . n= positive integerSec. 6,1; Prob. 31Ггр + 1)4. P.p> -1Sec. 6.1; Prob. 31S>05. sin ats>0See. 6.1; Ex. 76. cos atSec. 6.1; Prob. 6s>07. sinh ats> la|Sec. 6.1; Prob. 88. cosh atS> la|Sec. 6.1; Prob. 7b.9. sin btSec. 6.1; Prob. 13(s- a) + bS-a10. cos btSec. 6.1; Prob. 14(s- a)? + bn!11. e,n= positive integerSec. 6.1: Prob. 18(s- a)T12. 4(1)Sec. 6.313. u.()S(1 -)Sec. 6.314. fu)F(s- c)Sec. 6.3(). c>0Sec. 6.3; Prob. 2515. f(et)ra- ng()dtSec. 6.616.F)G)17. 31 - c)Sec. 6.518. f)*Fo)-s-0)-.-fa-(0)Sec. 6.2: Cor. 6.2.219. (-1"f)Fin (s)Sec. 6.2: Prob. 295.- in Problentransform methodts) Find the solution of the following differential equation using the Laplacey" + y = sin 2twhich satisfies the initial conditions y(0) = 2 and y'(0) = 1. (Use the Laplace transformtable in next page).

Answered: Image /qna-images/answer/291adbd6-add3-4a94-b199-cbbdaf4169fa.jpg

Problen ts) Find the solution of the following differential equation using the Laplace transform method y" + y = sin 2t which satisfies the initial conditions y(0) = 2 and y' (0) = 1. (Use the Laplace transform table in next page).

Problen ts) Find the solution of the following differential equation using the Laplace transform method y" + y = sin 2t which satisfies the initial conditions y(0) = 2 and y' (0) = 1. (Use the Laplace transform table in next page).

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

TABLE 6.2.1 Elementary Laplace Transforms
Fis) = LIS))
Notes
1. 1
s>0
Sec. 6.1; Ex. 4
2. e
Sec. 6.1; Ex. 5
n!
3. . n= positive integer
Sec. 6,1; Prob. 31
Ггр + 1)
4. P.
p> -1
Sec. 6.1; Prob. 31
S>0
5. sin at
s>0
See. 6.1; Ex. 7
6. cos at
Sec. 6.1; Prob. 6
s>0
7. sinh at
s> la|
Sec. 6.1; Prob. 8
8. cosh at
S> la|
Sec. 6.1; Prob. 7
b.
9. sin bt
Sec. 6.1; Prob. 13
(s- a) + b
S-a
10. cos bt
Sec. 6.1; Prob. 14
(s- a)? + b
n!
11. e,
n= positive integer
Sec. 6.1: Prob. 18
(s- a)T
12. 4(1)
Sec. 6.3
13. u.()S(1 -)
Sec. 6.3
14. fu)
F(s- c)
Sec. 6.3
(). c>0
Sec. 6.3; Prob. 25
15. f(et)
ra- ng()dt
Sec. 6.6
16.
F)G)
17. 31 - c)
Sec. 6.5
18. f)
*Fo)-s-0)-.-fa-(0)
Sec. 6.2: Cor. 6.2.2
19. (-1"f)
Fin (s)
Sec. 6.2: Prob. 29
5.
- in

Problen
transform method
ts) Find the solution of the following differential equation using the Laplace
y" + y = sin 2t
which satisfies the initial conditions y(0) = 2 and y'(0) = 1. (Use the Laplace transform
table in next page).

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