What is a solution to the differential equation $\frac{d y}{d x} = e^{x - y}$ $dy/dx=e^(x-y)$ ?

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Answer 1 · 2016-08-16T07:47:44

$y = ln (e^{x} + C)$ $y = ln( e^x + C)$

$\frac{d y}{d x} = e^{x - y}$ $dy/dx=e^(x-y)$
$= e^{x} \cdot e^{- y}$ $= e^x *e^-y$ we can separate it!

$e^{y} \frac{d y}{d x} = e^{x}$ $e^y dy/dx= e^x$

$int e^y dy/dx \ dx=int e^x \ dx$

$int e^y \ dy=int e^x \ dx$

$e^y = e^x + C$

$ln ( e^y) =ln( e^x + C)$

$y = ln( e^x + C)$

What is a solution to the differential equation dy/dx=e^(x-y)dydx=ex−ydy/dx=e^(x-y)?