Program Explanation Given information: The function is F ( s ) = s 2 − 2 s s 4 + 5 s 2 + 4 . Explanation: The given function is F ( s ) = s 2 − 2 s s 4 + 5 s 2 + 4 . Apply inverse Laplace transform to the function F ( s ) = s 2 − 2 s s 4 + 5 s 2 + 4 . L − 1 { F ( s ) } = L − 1 { s 2 − 2 s s 4 + 5 s 2 + 4 } = L − 1 { s 2 − 2 s s 4 + 4 s 2 + s 2 + 4 } = L − 1 { s 2 − 2 s s 2 ( s 2 + 4 ) + 1 ( s 2 + 4 ) } = L − 1 { s 2 − 2 s ( s 2 + 4 ) ( s 2 + 1 ) } Apply partial fraction method to solve the above expression, s 2 − 2 s ( s 2 + 4 ) ( s 2 + 1 ) = A s + B s 2 + 1 + C s + D s 2 + 4 …… (1) Multiply the equation by denominator as, s 2 − 2 s ( ( s 2 + 4 ) ( s 2 + 1 ) ) ( s 2 + 4 ) ( s 2 + 1 ) = ( A s + B ) ( ( s 2 + 4 ) ( s 2 + 1 ) ) s 2 + 1 + ( C s + D ) ( s 2 + 4 ) ( s 2 + 1 ) s 2 + 4 s 2 − 2 s = ( A s + B ) ( ( s 2 + 4 ) ) + ( C s + D ) ( s 2 + 1 ) s 2 − 2 s = A s 3 + 4 A s + B s 2 + 4 B + C s 3 + C s + D s 2 + D s 2 − 2 s = ( A s 3 + C s 3 ) + ( B s 2 + D s 2 ) + ( 4 A s + C s ) + ( 4 B + D ) Equating the coefficient of s 3 , s 2 , s and 1 shown below

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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Question

Chapter 7.3, Problem 19P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=s2−2ss4+5s2+4 by using partial fraction.

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Chapter 7.3, Problem 18P

Chapter 7.3, Problem 20P

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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 − 2 s s 4 + 5 s 2 + 4 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)=s2−2ss4+5s2+4 by using partial fraction.

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Chapter 7 Solutions