Chapter 6, Problem 19RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Solving a Differential Equation In Exercises 15–22, find the general solution of the differential equation. ( 2 + x ) y ' − x y = 0

To determine

To calculate: General solution of differential equation (2+x)y'xy=0.

Explanation

Given:

Differential equation: (2+x)y'âˆ’xy=0

Formula used:

Integration of 1x is given by:

âˆ«1xdx=lnx+C

Calculation:

Given equation can be written as

(2+x)y'=xyy'y=x(2+x)

Now integrate to both sides with dx

âˆ«y'ydx=âˆ«x(2+x)dx

And,

âˆ«dyy=âˆ«x(2+x)dx â€¦...â€¦... (1)

Letting z=2+x.

zâˆ’2=x

By differential both side

dz=dx

Now put values of z and dz in equation (1):

âˆ«dyy=âˆ«(zâˆ’2z)dz

And,

âˆ«dyy=

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