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

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

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

Publisher: PEARSON

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Problems on Growing Functions

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Question

Chapter 7.3, Problem 21P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=s2+3( s 2 +2s+2)2 by using partial fraction.

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Chapter 7.3, Problem 20P

Chapter 7.3, Problem 22P

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Chapter 7 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F ( s ) = s 2 + 3 ( s 2 + 2 s + 2 ) 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)=s2+3( s 2 +2s+2)2 by using partial fraction.

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Chapter 7 Solutions