University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.2 - Exponential Change and Separable Differential Equations - Exercises - Page 409: 11



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