Program Explanation Given information: The function is F ( s ) = 1 ( s 2 + s − 6 ) 2 . Explanation: The given function is F ( s ) = 1 ( s 2 + s − 6 ) 2 . Apply inverse Laplace transform to the function F ( s ) = 1 ( s 2 + s − 6 ) 2 . L − 1 { F ( s ) } = L − 1 { 1 ( s 2 + s − 6 ) 2 } = L − 1 { 1 ( s 2 + 3 s − 2 s − 6 ) 2 } = L − 1 { 1 ( s ( s + 3 ) + s ( s − 2 ) ) 2 } = L − 1 { 1 ( ( s − 2 ) ( s + 3 ) ) 2 } Apply partial fraction method to solve the above expression, 1 ( ( s − 2 ) ( s + 3 ) ) 2 = A s + B ( s + 3 ) 2 + C s + D ( s − 2 ) 2 …… (1) Multiply the equation by denominator as, 1 ( ( ( s − 2 ) ( s + 3 ) ) 2 ) ( ( s − 2 ) ( s + 3 ) ) 2 = ( A s + B ) ( ( ( s − 2 ) ( s + 3 ) ) 2 ) ( s + 3 ) 2 + C s + D ( ( ( s − 2 ) ( s + 3 ) ) 2 ) ( s − 2 ) 2 1 = ( A s + B ) ( s − 2 ) 2 + ( C s + D ) ( s + 3 ) 2 1 = ( A s + B ) ( s 2 − 4 s + 4 ) + ( C s + D ) ( s 2 + 6 s + 9 ) 1 = [ ( A s 3 + C s 3 ) + ( − 4 A s 2 + B s 2 + 6 C s 2 + D s 2 ) + ( 4 A s − 4 B s + 9 C s + 6 D s ) + ( 4 B + 9 D ) ] Equating the coefficient of s 3 , s 2 , s and 1 as, A + C = 0 − 4 A + B + 6 C + D = 0 4 A − 4 B + 9 C + 6 D = 0 4 B + 9 D = 1 Solve the above equation to obtain the value of A , B

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

Publisher: PEARSON

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Problems on Growing Functions

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Chapter 7.3, Problem 16P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1( s 2 +s−6)2 by using partial fraction.

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Chapter 7.3, Problem 15P

Chapter 7.3, Problem 17P

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Chapter 7 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F ( s ) = 1 ( s 2 + s − 6 ) 2 by using partial fraction.

Solution Summary: The author explains how to obtain the inverse Laplace transformation of the functions by using partial tion.

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=1( s 2 +s−6)2 by using partial fraction.

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Chapter 7 Solutions