Program Explanation Given information: The differential equation is, ( x − y ) y ′ = x + y Calculation: The given differential equation can be written as, d y d x = x + y x − y = x ( 1 + y x ) x ( 1 − y x ) = 1 + y x 1 − y x Substitute v = y x and differentiate with respect to x as, x v = y d d x ( x v ) = d y d x v d x d x + x d v d x = d y d x v + x d v d x = d y d x Now, the given differential equation can be written as, v + x d v d x = 1 + v 1 − v x d v d x = 1 + v 1 − v − v = 1 + v − v ( 1 − v ) 1 − v = 1 + v 2 1 − v Simplify the above equation as, 1 − v 1 + v 2 d v = d x x Integrate on both sides as, ∫ 1 − v 1 + v 2 d v = ∫ d x x + c Simplify above equation as, ∫ d v 1 + v 2 − ∫ v d v 1 + v 2 = ln x + C ......

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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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.

Question

Chapter 1.6, Problem 4P

Program Plan Intro

To calculate: The general solutions of the differential equation (x−y)y′=x+y .

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Chapter 1.6, Problem 3P

Chapter 1.6, Problem 5P

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Chapter 1 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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Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

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The general solutions of the differential equation ( x − y ) y ′ = x + y .

Solution Summary: The author explains the general solutions of the differential equation (x-y)xprime.

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To calculate: The general solutions of the differential equation (x−y)y′=x+y .

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Chapter 1 Solutions