   Chapter 8.2, Problem 34E

Chapter
Section
Textbook Problem

# Differential Equation In Exercises 35-38, find the general solution of the differential equation. d y d x = x 2 x − 3

To determine

To calculate: The general solution of the given differential equation,

dydx=x2x3.

Explanation

Given:

We have,

The given differential equation is, dydx=x2x3

Formula used:

By using Integration by parts,

We have,

udv=uvvdu.

Calculation:

We can write the given differential equation as ,

dydx=x2x3dy=x2x3dx

Now on taking integration both sides,

We have,

dy=x2x3dxy=x2x3dx+C

Now let I=x2x3dx

In order to integrate I by parts method

Let u=x2 and dv=x3dx.

On differentiating u and by integrating the 2nd one

we get,

du=2xdx

And

let

v=23(x3)32

By using integration by parts,

We have,

udv=uvvdu=x2{23(x3)32}{23(x3)32}(2xdx)=2x23(x3)3243x(x3)32dx

Again, now for the second part of integration

We are takeing u=x and dv=(x3)32dx,

using by parts of integration

Now again on Differentiating u and by integrating the 2nd one

We get

du=dx

And

### 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

#### Rationalize Numerator Rationalize the numerator. 91. 153

Precalculus: Mathematics for Calculus (Standalone Book)

#### Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### solve the equation by using the quadratic formula. 137. 8x2 8x 3 = 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 31-36, simplify each expression. 36.

Mathematical Applications for the Management, Life, and Social Sciences

#### Prove theorem 11.6.

Calculus: Early Transcendental Functions (MindTap Course List) 