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?$$x y^{\prime}=3 y-6 x^{2}$$

$y=6 x^{2}+C x^{3}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:15

What are the integrating f…

05:22

04:17

02:23

11:05

10:23

01:58

03:05

03:15

Section four Doubt five problem 225. We have a first order linear ordinary differential equation. OK, The standard form for this is why prime plus some function of X times Why equal some other function of X And then the integrating factor is going to be e and the anti derivative of P of x dx. So to get this in standard form, you're gonna have X Y prime minus three. Why equal minus six x squared. Divide everything by X. Why prime minus three over X. Why is equal to minus six X So that's standard form. And then my integrating factor is going to be e so the anti derivative of minus three over X dx. So this is E to the minus three natural log of X that is e to the natural log of X to the minus three. And so that is simply X to the minus three power. Yeah, So I need to take this equation which is in standard form and multiply both sides by one over X cubed. Okay, So when you multiply the entire equation, you're gonna have why times one over X cubed prime is equal to minus six. X time is one over execute. So this is why over X Cubed prime is equal to minus six over X squared. And now we are able to integrate both sides with respect to X. And we end up with why over X cubed it's equal to when you integrate this grunting end up with six over X plus a constant. Now you multiply everything on both sides of the equation by X cubed in order to solve for why should I get why is equal to six x squared plus c x cubed that is the family of solutions for this ordinary different your question.

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?

01:44

Match the direction field with the given differential equations. Explain you…

01:43

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

04:28

Find the area under the curve $y=\frac{1}{1+\sin x}$ between $x=0$ and $x=\p…

01:51

Find a function $f(n)$ that identifies the $n$ th term $a_{n}$ of the follow…

01:01

For the following exercises, solve the differential equations.Find the v…

01:36

Graph the curve $y=\frac{x}{1+x}$ over the interval $[0,5] .$ Then, find the…

03:22

Find the area under $y=\frac{5}{1+x^{2}}$ in the first quadrant.

06:31

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

01:25

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

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.