Program Explanation Given information: The differential function is x ( 3 ) + x ″ − 6 x ′ = 0 . The initial condition given as x ( 0 ) = 0 and x ′ ( 0 ) = x ″ ( 0 ) = 1 . Explanation: The given differential function is x ( 3 ) + x ″ − 6 x ′ = 0 . Apply Laplace transform to the function x ( 3 ) + x ″ − 6 x ′ = 0 . L { x ( 3 ) + x ″ − 6 x ′ } = L { 0 } L { x ( 3 ) } + L { x ″ } − L { 6 x } = L { ( 0 ) } [ ( s 3 x ( s ) − s 2 x ( s ) − s x ′ ( 0 ) − x ″ ( 0 ) ) + 4 ( s 2 x ( s ) − s x ( 0 ) − x ′ ( 0 ) ) − 6 ( s x ( s ) − x ( 0 ) ) ] = 0 Apply initial condition x ( 0 ) = 0 and x ′ ( 0 ) = x ″ ( 0 ) = 1 in above equation. [ ( s 3 x ( s ) − s 2 x ( s ) − s − 1 ) + 4 ( s 2 x ( s ) − s ( 0 ) − 1 ) − 6 ( s x ( s ) − ( 0 ) ) ] = 0 x ( s ) ( s 3 + s 2 − 6 s ) = s + 2 x ( s ) ( s 2 + 4 s + 8 ) = s + 2 s ( s 2 + 3 s − 2 s − 6 ) x ( s ) = s + 2 ( s ) ( s + 3 ) ( s − 2 ) Apply partial fraction method to solve the above expression, s + 2 ( s ) ( s + 3 ) ( s − 2 ) = A s + 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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Chapter 7.3, Problem 31P

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Program Description: Purpose of problem is to solve the initial value problem x(3)+x″−6x′=0 by using Laplace transformation.

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Chapter 7.3, Problem 30P

Chapter 7.3, Problem 32P

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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 solve the initial value problem x ( 3 ) + x ″ − 6 x ′ = 0 by using Laplace transformation.

Solution Summary: The author explains the purpose of the problem, which is to solve the initial value problem x(3)+

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Program Description: Purpose of problem is to solve the initial value problem x(3)+x″−6x′=0 by using Laplace transformation.

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Chapter 7 Solutions