The following shows the process of determining the inverse Laplace transform of s² +9s+2 Please fill all the blanks in the below. (Note that the answers must be (s−1)² (s+3) written as an integer format such as 1, 2, 3, -1, -2 etc.) . Solution Path: To find the inverse Laplace transform, we need to apply partial fraction as the following form B s²+9s+2 (S-1)² (s+3) A+ + (8-1)² We begin by multiplying both sides by (s − 1)² (s + 3), we have s² +9s + 2 = A(s − 1)(s + 3) + B(s+ 3) + C(s − 1)² From this, we can find A = 3 = 9 In here, D = 1 B = -1 Now that we have derived the partial fraction expansion for the given rational function, we can determine its inverse Laplace transform L-¹ { s²+9s+2 (S-1)² (s+3) = C s+3 -} = L− ¹ { ₁ + + , and C= 2 9 2 B (s-1)² AeDt + Bte Et + CeFt E = 1 2 s+3 and F = -3
The following shows the process of determining the inverse Laplace transform of s² +9s+2 Please fill all the blanks in the below. (Note that the answers must be (s−1)² (s+3) written as an integer format such as 1, 2, 3, -1, -2 etc.) . Solution Path: To find the inverse Laplace transform, we need to apply partial fraction as the following form B s²+9s+2 (S-1)² (s+3) A+ + (8-1)² We begin by multiplying both sides by (s − 1)² (s + 3), we have s² +9s + 2 = A(s − 1)(s + 3) + B(s+ 3) + C(s − 1)² From this, we can find A = 3 = 9 In here, D = 1 B = -1 Now that we have derived the partial fraction expansion for the given rational function, we can determine its inverse Laplace transform L-¹ { s²+9s+2 (S-1)² (s+3) = C s+3 -} = L− ¹ { ₁ + + , and C= 2 9 2 B (s-1)² AeDt + Bte Et + CeFt E = 1 2 s+3 and F = -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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Transcribed Image Text:The following shows the process of determining the inverse Laplace transform of
Please fill all the blanks in the below. (Note that the answers must be
s²+9s+2
(S-1)² (s+3)
written as an integer format such as 1, 2, 3, -1, -2 etc.)
Solution Path: To find the inverse Laplace transform, we need to apply partial
fraction as the following form
B
s²+9s+2
(s−1)² (s+3)
A₁+ +
(s−1)²
We begin by multiplying both sides by (s − 1)² (s + 3), we have
s² +9s + 2 = A(s − 1)(s+ 3) + B(s+ 3) + C(s — 1)²
From this, we can find
A =
3
=
9
L-¹{. s²+9s+2
In here, D = 1
B = -1
Now that we have derived the partial fraction expansion for the given rational
function, we can determine its inverse Laplace transform
-}
(s−1)²(s+3)
-
=
C
s+3
E =
9
L− ¹ { ₁ +
A
S
AeDt
1
and C = 2
B
(s−1)²
+ Bte Et
C
+s43}
+ CeFt
9
and F
-3
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