Program Explanation Given information: The system of linear differential equation is written as below. { x ′ = x + 2 y y ′ = x + e − t The initial value for the above differential equation is shown below. x ( 0 ) = 0 y ( 0 ) = 0 Calculation: Perform the Laplace transform on the differential equations and solve the equation as follows: { L { x ′ ( t ) } = L { x ( t ) + 2 y ( t ) } L { y ′ ( t ) } = L { x ( t ) + e − t } { L { x ′ ( t ) } = L { x ( t ) } + 2 L { y ( t ) } L { y ′ ( t ) } = L { x ( t ) } + L { e − t } Further simplify the above system of equations as, { ( s L { x ( t ) } − x ( 0 ) ) = L { x ( t ) } + 2 L { y ( t ) } ( s L { y ( t ) } − y ( 0 ) ) = L { x ( t ) } + 1 s + 1 { ( s L { x ( t ) } − ( 0 ) ) = L { x ( t ) } + 2 L { y ( t ) } ( s L { y ( t ) } − ( 0 ) ) = L { x ( t ) } + 1 s + 1 Further simplify the above system of equations as, { s L { x ( t ) } = L { x ( t ) } + 2 L { y ( t ) } s L { y ( t ) } = L { x ( t ) } + 1 s + 1 { ( s − 1 ) L { x ( t ) } − 2 L { y ( t ) } = 0 L { x ( t ) } − s L { y ( t ) } = − 1 s + 1 Solve the obtained system of equation by elimination method and obtain L { x ( t ) } and L { y ( t ) } as shown below. { L { x ( t ) } = 2 ( s + 1 ) 2 ( s − 2 ) L { y ( t ) } = s − 1 ( s + 1 ) 2 ( s − 2 ) Take the inverse Laplace transform of each equation and solve as follows: First, solve for the function x ( t ) as 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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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 12P

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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 11P

Chapter 7.2, Problem 13P

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Solve the initial value problem of the following DE using Laplace Transform

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

Ch. 7.1 - Prob. 11P Ch. 7.1 - Prob. 12P Ch. 7.1 - Prob. 13P Ch. 7.1 - Prob. 14P Ch. 7.1 - Prob. 15P Ch. 7.1 - Prob. 16P Ch. 7.1 - Prob. 17P Ch. 7.1 - Prob. 18P Ch. 7.1 - Prob. 19P Ch. 7.1 - Prob. 20P Ch. 7.1 - Prob. 21P Ch. 7.1 - Prob. 22P Ch. 7.1 - Prob. 23P Ch. 7.1 - Prob. 24P Ch. 7.1 - Prob. 25P Ch. 7.1 - Prob. 26P Ch. 7.1 - Prob. 27P Ch. 7.1 - Prob. 28P Ch. 7.1 - Prob. 29P Ch. 7.1 - Prob. 30P Ch. 7.1 - Prob. 31P Ch. 7.1 - Prob. 32P Ch. 7.1 - Prob. 33P Ch. 7.1 - Prob. 34P Ch. 7.1 - Prob. 35P Ch. 7.1 - Prob. 36P Ch. 7.1 - Given a0, let f(t)=1 if 0__1a,f(t)=0 if t__a....Ch. 7.1 - Given that 0ab. Let f(t)=1 if a__tb,f(t)=0 if...Ch. 7.1 - Prob. 39P Ch. 7.1 - Prob. 40P Ch. 7.1 - Prob. 41P Ch. 7.1 - Given constants a and b. define h(t) for t__0 by...Ch. 7.2 - Prob. 1P Ch. 7.2 - Prob. 2P Ch. 7.2 - Prob. 3P Ch. 7.2 - Prob. 4P Ch. 7.2 - Prob. 5P Ch. 7.2 - Prob. 6P Ch. 7.2 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 10P Ch. 7.2 - Prob. 11P Ch. 7.2 - Prob. 12P Ch. 7.2 - Prob. 13P Ch. 7.2 - Prob. 14P Ch. 7.2 - Prob. 15P Ch. 7.2 - Prob. 16P Ch. 7.2 - Prob. 17P Ch. 7.2 - Prob. 18P Ch. 7.2 - Prob. 19P Ch. 7.2 - Prob. 20P Ch. 7.2 - Prob. 21P Ch. 7.2 - Prob. 22P Ch. 7.2 - Prob. 23P Ch. 7.2 - Prob. 24P Ch. 7.2 - Prob. 25P Ch. 7.2 - Prob. 26P Ch. 7.2 - Prob. 27P Ch. 7.2 - Prob. 28P Ch. 7.2 - Prob. 29P Ch. 7.2 - Prob. 30P Ch. 7.2 - Prob. 31P Ch. 7.2 - Prob. 32P Ch. 7.2 - Prob. 33P Ch. 7.2 - Prob. 34P Ch. 7.2 - Prob. 35P Ch. 7.2 - Prob. 36P Ch. 7.2 - Prob. 37P Ch. 7.3 - Prob. 1P Ch. 7.3 - Prob. 2P Ch. 7.3 - Prob. 3P Ch. 7.3 - Prob. 4P Ch. 7.3 - Prob. 5P Ch. 7.3 - Prob. 6P Ch. 7.3 - Prob. 7P Ch. 7.3 - Prob. 8P Ch. 7.3 - Prob. 9P Ch. 7.3 - Prob. 10P Ch. 7.3 - Prob. 11P Ch. 7.3 - Prob. 12P Ch. 7.3 - Prob. 13P Ch. 7.3 - Prob. 14P Ch. 7.3 - Prob. 15P Ch. 7.3 - Prob. 16P Ch. 7.3 - Prob. 17P Ch. 7.3 - Prob. 18P Ch. 7.3 - Prob. 19P Ch. 7.3 - Prob. 20P Ch. 7.3 - Prob. 21P Ch. 7.3 - Prob. 22P Ch. 7.3 - Prob. 23P Ch. 7.3 - Prob. 24P Ch. 7.3 - Prob. 25P Ch. 7.3 - Prob. 26P Ch. 7.3 - Prob. 27P Ch. 7.3 - Prob. 28P Ch. 7.3 - Prob. 29P Ch. 7.3 - Prob. 30P Ch. 7.3 - Prob. 31P Ch. 7.3 - Prob. 32P Ch. 7.3 - Prob. 33P Ch. 7.3 - Prob. 34P Ch. 7.3 - Prob. 35P Ch. 7.3 - Prob. 36P Ch. 7.3 - Prob. 37P Ch. 7.3 - Prob. 38P Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.4 - Find the convolution f(t)g(t) in Problems 1...Ch. 7.4 - Prob. 2P Ch. 7.4 - Prob. 3P Ch. 7.4 - Prob. 4P Ch. 7.4 - Prob. 5P Ch. 7.4 - Prob. 6P Ch. 7.4 - Prob. 7P Ch. 7.4 - Prob. 8P Ch. 7.4 - Prob. 9P Ch. 7.4 - Prob. 10P Ch. 7.4 - Prob. 11P Ch. 7.4 - Prob. 12P Ch. 7.4 - Prob. 13P Ch. 7.4 - Prob. 14P Ch. 7.4 - Prob. 15P Ch. 7.4 - Prob. 16P Ch. 7.4 - Prob. 17P Ch. 7.4 - Prob. 18P Ch. 7.4 - Prob. 19P Ch. 7.4 - Prob. 20P Ch. 7.4 - Prob. 21P Ch. 7.4 - Prob. 22P Ch. 7.4 - Prob. 23P Ch. 7.4 - Prob. 24P Ch. 7.4 - Prob. 25P Ch. 7.4 - Prob. 26P Ch. 7.4 - Prob. 27P Ch. 7.4 - Prob. 28P Ch. 7.4 - Prob. 29P Ch. 7.4 - Prob. 30P Ch. 7.4 - Prob. 31P Ch. 7.4 - Prob. 32P Ch. 7.4 - Prob. 33P Ch. 7.4 - Prob. 34P Ch. 7.4 - Prob. 35P Ch. 7.4 - Prob. 36P Ch. 7.4 - Prob. 37P Ch. 7.4 - Prob. 38P Ch. 7.4 - Prob. 39P Ch. 7.4 - Prob. 40P Ch. 7.4 - Prob. 41P Ch. 7.5 - Prob. 1P Ch. 7.5 - Prob. 2P Ch. 7.5 - Prob. 3P Ch. 7.5 - Prob. 4P Ch. 7.5 - Prob. 5P Ch. 7.5 - Prob. 6P Ch. 7.5 - Prob. 7P Ch. 7.5 - Prob. 8P Ch. 7.5 - Prob. 9P Ch. 7.5 - Prob. 10P Ch. 7.5 - Prob. 11P Ch. 7.5 - Prob. 12P Ch. 7.5 - Prob. 13P Ch. 7.5 - Prob. 14P Ch. 7.5 - Prob. 15P Ch. 7.5 - Prob. 16P Ch. 7.5 - Prob. 17P Ch. 7.5 - Prob. 18P Ch. 7.5 - Prob. 19P Ch. 7.5 - Prob. 20P Ch. 7.5 - Prob. 21P Ch. 7.5 - Prob. 22P Ch. 7.5 - Prob. 23P Ch. 7.5 - Prob. 24P Ch. 7.5 - Prob. 25P Ch. 7.5 - Prob. 26P Ch. 7.5 - Let g(t) be the staircase function of Fig. 7.5.15....Ch. 7.5 - Suppose that f(i) is a periodic function of period...Ch. 7.5 - Suppose that f(t) is the half-wave rectification...Ch. 7.5 - Let g(t)=u(tk)f(tk), where f(t) is the function of...Ch. 7.5 - Prob. 31P Ch. 7.5 - Prob. 32P Ch. 7.5 - Prob. 33P Ch. 7.5 - Prob. 34P Ch. 7.5 - Prob. 35P Ch. 7.5 - Prob. 36P Ch. 7.5 - Prob. 37P Ch. 7.5 - Prob. 38P Ch. 7.5 - Prob. 39P Ch. 7.5 - Prob. 40P Ch. 7.5 - Prob. 41P Ch. 7.5 - Prob. 42P Ch. 7.6 - Prob. 1P Ch. 7.6 - Prob. 2P Ch. 7.6 - Prob. 3P Ch. 7.6 - Prob. 4P Ch. 7.6 - Prob. 5P Ch. 7.6 - Prob. 6P Ch. 7.6 - Prob. 7P Ch. 7.6 - Prob. 8P Ch. 7.6 - Prob. 9P Ch. 7.6 - Prob. 10P Ch. 7.6 - Prob. 11P Ch. 7.6 - Prob. 12P Ch. 7.6 - Prob. 13P Ch. 7.6 - Prob. 14P Ch. 7.6 - This problem deals with a mass in on a spring...Ch. 7.6 - Prob. 16P Ch. 7.6 - Prob. 17P Ch. 7.6 - Prob. 18P Ch. 7.6 - Prob. 19P Ch. 7.6 - Repeat Problem 19, except suppose that the switch...Ch. 7.6 - Prob. 21P Ch. 7.6 - Prob. 22P

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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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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