Program Explanation Given information: The differential equation is x 3 y ′ = x 2 y − y 3 . Explanation: The given differential equation can be written as, d y d x = x 2 y − y 3 x 3 = y x − y 3 x 3 The above equation is a homogeneous equation. Consider v = y x and differentiate with respect to x . d d x ( v x ) = d y d x v + x d v d x = d y d x The given differential equation can be written as, v + x d v d x = v − v 3 x d v d x = − v 3 d v v 3 = − d x x Integrate both sides of above equation. ∫ v − 3 d v = − ln x + C v − 2 − 2 = − ln x + C − 1 2 v 2 = ln x + C Simplify the above equation

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 1, Problem 14RP

Program Plan Intro

Program Description: Purpose of problem is to calculate the general solution of the differential equation x3y′=x2y−y3 .

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Chapter 1, Problem 13RP

Chapter 1, Problem 15RP

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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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Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - 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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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Program Description: Purpose of problem is to calculate the general solution of the differential equation x 3 y ′ = x 2 y − y 3 .

Solution Summary: The author explains that the differential equation is a homogeneous equation.

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x3y′=x2y−y3 .

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Chapter 1 Solutions