Program Explanation Given information: The differential equation is ( x + 2 y ) y ′ = y . Calculation: The given differential equation can be written as, d y d x = y ( x + 2 y ) = y x ( 1 + 2 y x ) = y x 1 + 2 y x Substitute v = y x and differentiate with respect to x as, x v = y d d x ( x v ) = d y d x v d x d x + x d v d x = d y d x v + x d v d x = d y d x Now, the given differential equation can be written as, v + x d v d x = v 1 + 2 v x d v d x = v 1 + 2 v − v = v − v ( 1 + 2 v ) 1 + v = v − v − 2 v 2 1 + v Simplify the above equation. x d v d x = − 2 v 2 1 + 2 v 1 + 2 v − 2 v 2 d v = d x x − 1 2 ( 1 + 2 v v 2 ) d v = d x x Integrate on both sides as, − 1 2 ∫ 1 + 2 v v 2 d v = ∫ d x x − 1 2 &#

5th Edition

ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 1.6, Problem 6P

Program Plan Intro

To calculate: The general solutions of the differential equation (x+2y)y′=y .

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Chapter 1.6, Problem 5P

Chapter 1.6, Problem 7P

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Chapter 1 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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The general solutions of the differential equation ( x + 2 y ) y ′ = y .

Solution Summary: The author explains the general solutions of the differential equation (x+2y)y

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To calculate: The general solutions of the differential equation (x+2y)y′=y .

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Chapter 1 Solutions