Explanation Given: The given differential equation is x d y d x = y + x 2 − y 2 and the initial condition y ( 5 ) = 0 . Calculation: Consider the differential equation, x d y d x = y + x 2 − y 2 … … ( 1 ) Consider the equation, y = u x … … ( 2 ) Differentiate equation (2). d y d x = u + x d u d x Substitute u + x d u d x for d y d x in equation (1). x ( u + x d u d x ) = u x + ( x 2 − ( u x ) 2 ) ( u + 1 − u 2 ) d x − ( u d x + x d u ) = 0 1 − u 2 d x − x d u = 0 … … ( 3 ) Integrate equation (3)

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.5, Problem 33E

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To explain: The reason to express the homogenous equation in the form dydx=f(yx) and find the largest interval.

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Chapter 2.5, Problem 32E

Chapter 2.5, Problem 34E

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A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...

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The reason to express the homogenous equation in the form d y d x = f ( y x ) and find the largest interval.

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To explain: The reason to express the homogenous equation in the form dydx=f(yx) and find the largest interval.

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Chapter 2 Solutions