Program Explanation Given information: The differential equation is, x y ′ = y + 2 x y Calculation: The given differential equation can be written as, y ′ = y + 2 x y x = y x + 2 x y x = y x + 2 y x Consider v = y x and differentiate with respect to x as, v x = y d d x ( v x ) = 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 + 2 v x d v d x = 2 v d v 2 v = d x x Integrate on both sides as, ∫ d v 2 v = ∫

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

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 3P

Program Plan Intro

To calculate: The general solution of the differential equation xy′=y+2xy .

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Chapter 1.6, Problem 2P

Chapter 1.6, Problem 4P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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The general solution of the differential equation x y ′ = y + 2 x y .

Solution Summary: The author explains the general solution of the differential equation xyprime =y+2sqrtxy.

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To calculate: The general solution of the differential equation xy′=y+2xy .

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Chapter 1 Solutions