## University Calculus: Early Transcendentals (3rd Edition)

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