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

$$e^{v}-e^{x}=C$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

Integrals and Transcendental Functions

Section 2

Exponential Change and Separable Differential Equations

Functions

Trig Integrals

Campbell University

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Idaho State University

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Lectures

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Solve the differential equ…

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Solve the given differenti…

03:42

02:46

01:23

01:30

Find the general solution …

02:29

you want to solve the differential equation here? So this is separable because knows we can rewrite this because e to the X over e to the y. So if we were to multiply each side of this equation by eat the why we're going to get e to the y, do you? Why, by d x is equal to eat the X Now we can multiply dx over and I say Multiply DX and quotes. I really can't. There's other reasons why it works out, though Now we will want to integrate. Each side will eat the y any to the extra. Just going to be eating the wind e to the X Better eternally give us anything too interesting extra money to Miko to stink So easy X plus C now to get why let's just take match log of each side so that gives us why is equal to the natural log of eat the X plus. See, So this here will be our solution

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