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

$y=x \ln |x|+C x$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:23

What are the integrating f…

03:05

04:17

11:05

02:15

02:10

05:22

10:23

00:58

in this video we are going to solve this differential equation Y. Prime minus why? Over a. Sorry? Y over X equals one. This is a standard form first we fi integrating factor P is -1 over X. So we integrated this and we get E. To the minus log of absolute eggs. This become one over absolute eggs, right? Yeah. Now we multiply both sides with this. And again we treat we can treat the absolute value as does no more polynomial because we have them on both sides. So when they are minors, they're all minors. And so it just Like we have -1 multiply on both sides and it cancel each other out. So the left side here become why times 10. X. And this thing prime. Yeah Equal one over X. So if we integrate both side we have Y. Times one or eggs equals integrate this. The X. Is just love absolute X. Right Plus C. Yeah soul. Our function Y. Is X. Time long, absolute eggs plus see you bigs. And that is the answer. Thank you.

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