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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Question
Transcribed Image Text: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
Transcribed Image Text: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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