(a) Explanation Given: The differential equation is d y d x = y 2 − x 2 x y and initial condition is y ( 1 ) = − 2 . Calculation: Consider the differential equation. d y d x = y 2 − x 2 x y (1) Consider the following substitution. y = u x (2) Differentiate equation (2) with respect to x . d y d x = u + x d u d x Substitute u x for y and u + x d u d x for d y d x in equation (1). u + x d u d x = ( u x ) 2 − x 2 x ( u x ) u + x d u d x = u 2 x 2 − x 2 u x 2 u + x d u d x = x 2 ( u 2 − 1 ) u x 2 x d u d x = ( u 2 − 1 ) u − u Further solving, x d u d x = ( u 2 − 1 ) − u 2 u x d u d x = − 1 u u d u = − d x x (3) Integrate equation (3) (b) To determine The largest interval I on which the solution is defined.

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

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, Problem 36RE

(a)

To determine

To solve: The initial-value problem for implicit solution.

(b)

To determine

The largest interval I on which the solution is defined.

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Chapter 2, Problem 35RE

Chapter 2, Problem 37RE

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Differential Equations with Boundary-Value Problems (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 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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The initial-value problem for implicit solution.

Solution Summary: The author explains the implicit solution of the initial-value problem. The initial condition is y(1)=-sqrt.