Chapter 6, Problem 22RE

### 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. y ' + x y = 9 x

To determine

To calculate: General solution of differential equation y'+xy=9x.

Explanation

Given:

Differential equation: y'+xy=9x

Formula used:

âˆ«xndx=xn+1n+1+c

Calculation:

Given equation can be written as

y'=9xâˆ’xyy'=x(9âˆ’y)y'9âˆ’y=x

Now integrate to both sides with dx

âˆ«y'9âˆ’ydx=âˆ«xdxâˆ’âˆ«y'yâˆ’9dx=âˆ«xdxâˆ’âˆ«dyyâˆ’9=âˆ«xdx â€¦...â€¦... (Asâ€‰â€‰â€‰dy=y'dx) (1)

Let z=yâˆ’9

By differential both side

dz=dy

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

âˆ’

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (3x+1)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Show that ddx1+tanhx1tanhx4=12ex/2.

Single Variable Calculus: Early Transcendentals, Volume I

#### In problems 1-16, solve each equation. 20.

Mathematical Applications for the Management, Life, and Social Sciences

#### In Exercises 3538, find the transpose of each matrix. [1264232562304502]

Finite Mathematics for the Managerial, Life, and Social Sciences