Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 11



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