Answer
$e^y-e^x=c$
Work Step by Step
As we are given that $\dfrac{dy}{dx}=e^{x-y}=\dfrac{e^x}{e^y}$
Re-arrange the given equation as follows:
$(e^y) dy=(e^x) dx$
Now take the help of integration.
Then $\int(e^y) dy= \int (e^x) dx \implies e^y=e^x+c$
Hence, $e^y-e^x=c$
