Program Explanation Given information: The differential equation is x y ′ − y = x and the initial condition is y ( 1 ) = 7 . Calculation: The given differential equation is x y ′ − y = x . The given differential equation can be written in the general linear differential equation as, x y ′ − y = x x x y ′ − y x = x x y ′ − y x = 1 Compare the given differential equation with a general linear differential equation to obtain the value of P ( x ) , Q ( x ) P ( x ) = − 1 x , Q ( x ) = 1 Now find the integrating factor IF as, IF = e ∫ p ( x ) d x = e ∫ − 1 x ⋅ d x = e − ln x = x − 1 Now substitute e x for IF , 2 for Q ( x ) in equation (1) to obtain the general solution

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 1.5, Problem 9P

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Program Description: The purpose of the problem is to find the particular solution of the differential equation xy′−y=x .

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Chapter 1.5, Problem 8P

Chapter 1.5, Problem 10P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: The purpose of the problem is to find the particular solution of the differential equation x y ′ − y = x .

Solution Summary: The author explains that the problem is to find the particular solution of the differential equation xyprime -y=x.

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Program Description: The purpose of the problem is to find the particular solution of the differential equation xy′−y=x .

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Chapter 1 Solutions