Program Explanation Given information: The differential equation is 2 x y + x 2 y ′ = y 2 . Explanation: The given differential equation can be written as, x 2 d y d x = y 2 − 2 x y d y d x = y 2 − 2 x y x 2 = y 2 x 2 − 2 ⋅ y x 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 2 − 2 v x d v d x = v 2 − 3 v d v v 2 − 3 v = d x x Integrate both sides of above equation. ∫ d v v 2 − 3 v = ∫ d x x Simplify the above equation. ∫ 1 v ( v − 3 ) d v = ln x + C ....... (1) Simplify the partial fraction 1 v ( v − 3 ) as, 1 v ( v − 3 ) = A v + B v − 3 = A v − 3 A + B v v ( v − 3 ) = ( A + B ) v − 3 A v ( v − 3 ) The value of A is calculated as, − 3 A = 1 A = − 1 3 The value of B is calculated as,</

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 8RP

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation 2xy+x2y′=y2 .

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Chapter 1, Problem 7RP

Chapter 1, Problem 9RP

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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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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation 2 x y + x 2 y ′ = y 2 .

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

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Program Description: Purpose ofproblem is to calculate the general solution of the differential equation 2xy+x2y′=y2 .

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Chapter 1 Solutions