Program Explanation Given information: The liner differential equation is written as below. x ″ + 4 x ′ + 3 x = 1 The initial value for the above differential equation is shown below. x ( 0 ) = 0 x ' ( 0 ) = 0 Calculation: Perform the Laplace transform on the differential equation and solve the equation as, L { x ″ ( t ) + 4 x ′ ( t ) + 3 x ( t ) } = L { 1 } L { x ″ ( t ) } + 4 L { x ′ ( t ) } + 3 L { x ( t ) } = 1 s Further simplify the above equation as, ( s 2 L { x ( t ) } − s x ( 0 ) − x ′ ( 0 ) ) + 4 ( s L { x ( t ) } − x ( 0 ) ) + 3 L { x ( t ) } = 1 s ( s 2 L { x ( t ) } − s ( 0 ) − ( 0 ) ) + 4 ( s L { x ( t ) } − ( 0 ) ) + 3 L { x ( t ) } = 1 s s 2 L { x ( t ) } + 4 s L { x ( t ) } + 3 L { x ( t ) } = 1 s L { x ( t ) } ( s 2 + 4 s + 3 ) = 1 s Further simplify the above equation with the use of inverse Laplace transform as, L { x ( t ) } = 1 s

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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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 7.2, Problem 9P

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Program Description: Purpose of the problem is to obtain the solution of initial value problem by the use of Laplace transforms.

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Chapter 7.2, Problem 8P

Chapter 7.2, Problem 10P

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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

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 the problem is to obtain the solution of initial value problem by the use of Laplace transforms.

Solution Summary: The author explains the purpose of the problem, which is to obtain the solution of initial value problem by the use of Laplace transforms.

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Program Description: Purpose of the problem is to obtain the solution of initial value problem by the use of Laplace transforms.

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Chapter 7 Solutions