💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Solve the following differential equations. Use your calculator to draw a family of solutions. Are there certain initial conditions that change the behavior of the solution?$$(x+2) y^{\prime}=2 y-1$$

$$y=\frac{1}{2}+C(x+2)^2$$The solutions change their behaviors on using $y(0)=\frac{1}{2}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Kemal T.

December 3, 2021

(2y-3x)dx+xdy=0

Emrah A.

January 3, 2022

gvb

(2y-10x)dx+xdy=0

Missouri State University

Oregon State University

University of Nottingham

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:01

Solve the following differ…

03:41

04:14

03:02

03:21

03:45

03:00

02:10

Solve the differential equ…

01:45

02:04

Find the solution of the g…

Section 45 problem to 33. So here I have an ordinary differential equation that I'm asked to solve. The first step is to put this in standard form. So that is why prime plus some function of X times why is equal to some other function of X, and then the integrating factor will be e to the anti derivative of P of X dx. So to get it in that form, any demort divide everything by X plus two. Some have y prime minus two over X Plus two. Why is equal to minus one over X plus two? And now the integrating factor is going to be e. And then you integrate, um to over X plus two d X with a minus signing there. And so that's just e to the minus two natural log of X plus two. And this just turns out to be one over X plus two quantity squared. So that tells me that this differential equation can be written as why over X plus two squared prime is equal to minus one over X plus two times one over X plus two squared. And so this gives me why over X plus two squared prime is equal to minus one over X plus two cube. And now I will integrate both sides of this equation. So on the left, I end up with why over X plus two squared and on the right, When I integrate one over X plus two Cube, this is going to give me 1/2 over X plus two squared, plus a constant of integration. And now you simply multiply everything on both sides of equation by X plus two. So you end up with y is equal to 1/2 plus a constant times X plus two square. So that is my solution. We're gonna look at this graphically, but look at this. So what you see here is you have a constant term, and then you have a quadratic term. So if c is positive, this is a problem. But open, separate see is negative. This is a problem opens downward. CIA zero. This is just a straight line. And so that's what I graphs should reflect for us. And so let's just look at this. So when C is negative downward opening Parabellum when C is equal to zero, the class of changed. The class of this function changes because that's just the line. Um, Why equal? Negative should be white, like wool. Negative 1/2. Um, and sorry about that. This is a positive. That should be a plus. Um, if I can change, this should be a positive at y equal 1/2. And then when c is positive, I have upward opening problem again. This would be the class of solutions for this different your question.

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…

Solve the following differential equations. Use your calculator to draw a fa…

Solve the differential equation by separation of variables. Where reasonable…

Find the solution of the given differential equation satisfying the indicate…