Explanation The differential equation is x y ′ = y + x e y x . Rewrite the differential equation x y ′ = y + x e y x as shown below. x y ′ = y + x e y x y ′ = y x + e y x Use the substitution v = y x and obtain the expression for y ′ as shown below. v = y x y = v x y ′ = v + x v ′ Substitute y ′ = v + x v ′ in y ′ = y x + e y x and the following is obtained. y ′ = y x + e y x v + x v ′ = v + e v ( ∵ v = y x ) x v ′ = e v v ′ e − v = 1 x Integrate the equation x v ′ = e v as shown below

Elementary Differential Equations and Boundary Value Problems, Enhanced

11th Edition

ISBN: 9781119381648

Author: Boyce

Publisher: WILEY

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Question

Chapter 2, Problem 20MP

To determine

The solution of the differential equation $xy′=y+xeyx$ .

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Chapter 2, Problem 19MP

Chapter 2, Problem 21MP

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Chapter 2 Solutions

Elementary Differential Equations and Boundary Value Problems, Enhanced

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The solution of the differential equation x y ′ = y + x e y x .

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Chapter 2 Solutions