## Thomas' Calculus 13th Edition

$e^y-e^x=c$
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, $e^y-e^x=c$