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Solving a Homogeneous Differential Equation In Exercises 77-82, solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form M ( x , y ) d x + N ( x , y ) d y = 0 where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = v x and d y = x d v + v d x . ( x 3 + y 3 ) d x − x y 2 d y = 0

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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275347
BuyFind

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275347

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Chapter
Section
Chapter 6.3, Problem 78E
Textbook Problem

Solving a Homogeneous Differential Equation In Exercises 77-82, solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form

M ( x , y ) d x + N ( x , y ) d y = 0

where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = v x and d y = x d v + v d x .

( x 3 + y 3 ) d x x y 2 d y = 0

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Calculus (MindTap Course List)
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