Answer
$e^y-e^x=c$
Work Step by Step
Given: $\dfrac{dy}{dx}=e^{x-y}=\dfrac{e^x}{e^y}$
This can be re-written as:
$e^y dy=e^x dx$
We need to integrate the above expression.
we have $\int e^y dy= \int e^x dx$
This implies that $e^y=e^x+c$
Thus,
$e^y-e^x=c$
