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Solve the differential equation.$$\frac{d y}{d x}=\frac{e^{2 x-y}}{e^{x+y}}$$

$ y = \frac{1}{2} ln(2e^x +C) $

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

Integrals and Transcendental Functions

Section 2

Exponential Change and Separable Differential Equations

Functions

Trig Integrals

Missouri State University

University of Nottingham

Idaho State University

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Lectures

01:11

In mathematics, integratio…

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In grammar, determiners ar…

01:16

Solve the differential equ…

00:31

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04:17

02:19

01:44

00:38

03:18

04:40

Solve the given differenti…

03:41

you saw this differential equation here. Now let's go ahead and simplify our right hand side. Is this gonna be eat the two X finest Y minus X plus? Why? So that's going to give us that. Do I? Let me stop it. Better D Y by the X is equal to looks like it'll be e to the X minus two. Why now We can multiply each side of this equation by eat too. Why as well as DX. And this should give us that on the left hand side e to the A to y Do you? Why is it to e to the X Times DX Now we'll just go ahead and integrate each side and integrating e to the two. Why? So that should be easy to the two. Why? And then we divide by its power and on the right hand side Well, this should just be e to the X plus C. Now we're gonna want to multiply, and I shall call the C one first because we may have a couple of Constance that papa. So let's go ahead and multiply each side of the square by two. So did he. To the two. Why is it, too, to e to the X Lost small C. One times two is just a Constance. Let's call that C two now. We could go ahead and take a natural log on each side and let me go ahead and actually expand screen a little bit. I'll move this up here. That should give us two. Why is equal to natural law? Go to he to the X Plus C two. And now let's divide each side by two. And so that should give why is equal to natural log of to E to the X must see to all over to end. Since we're done doing stuff with our constant, let's go ahead and get rid of the sea to and destroyed it as C so this will be our so

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