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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
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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
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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