Differential Equations Problems

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It is differential equations problems. It is the inverse Laplace transform. Only do #3,#4,#6,#7,#8,#10,#13,#16,#17& #19

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PROBLEMS: Section 5.3
For Problems 1-20, find the inverse Laplace transform of the given function.
1
1.
3
+
2. s
5
S
3.s? + 3
3
4
+
4.
$ + 3
10.
5. s2 + 38
$ + 1
6. 52 + 2s + 10
1
7.s? + 4s + 4
1
8. s? + 4s + 4
1
9.s
+-2
5
6
2s + 4
11.11
7
12. (8 + 2) + 3
28 + 16
13. +48 + 13
6
14. (8 + 2)
78 +238 + 30
15. (8 – 2 + 25 + 5)
4
16. (+4)
3
17.( + 16 + 4)
78 –
18. (8 + 1X + 2x – 3)
** – 2
19.
19.5+ 8 + 78
8 +95 +2
operational problem on actually finding ine inverse Laplace transiorm or a given iuncuon.
ansform as a function of F(s)? If we could turn this integral formula around, we would have a fo
se formula for finding f(t) in terms of F(s), the formula involves a contour integral over a re
avoid complex variable theory by simply using a table of Laplace transforms, such as Table 5. .
nply locate F(s) under the transform column and read off the corresponding function in the f(t)
y to find inverse transforms.
Laplace transform
Common inverse Laplace transforms
{L
S
1. 2-1
0-
= 1
= cos br
+ b2
n!
5. l-1
s2
b
6. 2-1
52 – 52
2. l-1
=1″
sinh bị
s
3. L-1
-}-
ear
7. L-1
= cosh br
– b?
–
S
b
4. L-1
해
= sin br
+ b 2
e inverse Laplace transforms of the following functions.

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Tags:
inverse Laplace transform

partial fraction

Inverse transform

constante multiplication property

transforming the equation

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