Find the solution of the following differential equations. dy=e^{x-y}dx

abreviatsjw 2021-12-28 Answered
Find the solution of the following differential equations.
dy=exydx
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Expert Answer

Esther Phillips
Answered 2021-12-29 Author has 34 answers
Step 1
dy=exydx
dy=exeydx
dyey=exdz
Step 2
eydy=exdx
Integrting both side
eydy=exdx.
ey=ex+c
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Jimmy Macias
Answered 2021-12-30 Author has 30 answers
In this tutorial we shall evaluate the simple differential equation of the form dydx=exy using the method of separating the variables.
The differential equation of the form is given as
dydx=exy
dydx=exey
dydx=exey
Separating the variables, the given differential equation can be written as
eydy=exdx (i)
In the separating the variables technique we must keep the terms dy and dx in the numerators with their respective functions.
Now integrating both sides of the equation (i), we have
eydy=exdx
Using the formulas of integration exdx=ex, we get
ey=ex+c
y=ln(ex+c)
This is the required solution of the given differential equation.
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Vasquez
Answered 2022-01-09 Author has 460 answers

dy=exydxdy=exeydxdyey=exdzeydy=exdxeydy=exdx.ey=ex+c

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