Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

What are the integrating factors for the following differential equations?$$y^{\prime}=3 x+x y$$

$y=-3+C e^{\frac{x^{2}}{2}}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Missouri State University

Campbell University

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:23

What are the integrating f…

05:22

02:15

10:23

01:58

03:05

02:53

11:05

02:10

section 4.5 problem 227. So we're dealing with ordinary differential equations that can be written in standard forms. If I can write an equation like this, why prime plus some function of X y equals some function of X? Then I can integrate this using an integrating factor. So let's get this in standard form. So it's going to be why prime minus X y equal three x So the integrating factor is going to be e toothy integral minus X dx. So this is going to be e to the minus. X squared over two is the integrating factor. So I need to multiply both sides of this equation by the integrating factor. So when I do that, why prime minus X y equals three acts? I won't buy all of that by e to the minus X squared over two. What you end up on the left side of the equation is just y e to the minus X squared over two. Prime is equal to three x e to the minus X squared over two, and then we can go ahead and look and say, Okay, what would it take them to integrate both sides of this equation. So when you integrate both sides of this equation on the left side of the equation, you're going to get why e to the minus x squared over two? Uh huh. And then what we have on the right side of the equation? It might help if I write this as, um three. Then I could write it as, what, minus two x. So put a negative in front of their this and he to the minus. Excuse me? X squared over two. So if I did appreciate that um, good. Um, just minus X, sir. Let me back up. Sorry. Let's do it like this. So I'm trying to do too many steps at one time. So what I can do here is make a substitution. If I let you equals e to the minus X squared over two, then do you is e to the minus. So that's minus two X over to e to the minus. X. Um, pardon me. I'm every day, different day here. So if you differentiate that you're going to get e to the minus X squared over two when you different shape minus x squared over to you get minus X. So what you see here is minus X dx and that in a row. So what this becomes is why e to the minus X squared over two is equal to minus three. And this is just the integral of e to the u. You did that you do you? So this is just minus three. He today you plus a constant of integration. So my answer here is why e to the minus x squared over two. The quota minus three you to the minus X squared over two plus a constant of integration. Now you divide everything by e to the minus x squared over to you get wise, you know, minus three plus c e to the X squared over two that is the family of functions that serve as the solution for this different equation.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

What are the integrating factors for the following differential equations?

02:05

Find the solution to the initial-value problem.$$y^{\prime}=-2 x \tan (y…

06:23

Find the volume generated by revolving the area bounded by $y=\frac{1}{x^{3}…

06:11

For the following problems, use a software program or your calculator to gen…

06:35

Use substitution to convert the integrals to integrals of rational functions…

02:36

Solve the following initial-value problems by using integrating factors.…

00:54

Write the following first-order differential equations in standard form.…

05:55

For the following exercises, evaluate the definite integrals. Express answer…

01:43

Differential equations can be used to model disease epidemics. In the next s…

03:20

00:17

Use the comparison test to determine whether the following series converge. …

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.