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: 18



Work Step by Step

Given: $\dfrac{dy}{dx}=\dfrac{e^{2x-y}}{e^{x+y}}$ Re-arrange the given equation and integrate as follows:. Then $\dfrac{dy}{dx}= \int e^{2x-y-x-y} \implies \int \dfrac{dy}{dx}= \int\dfrac{e^x}{e^{2y}} $ or, $\int e^{2y} dy =\int e^x dx$ ....(1) As we know that $\int x^n dx=\dfrac{x^{n+1}}{n+1}+c$ Equation (1) becomes: $ \dfrac{1}{2} e^{2y}=e^x+c$ Hence, $(\dfrac{1}{2})e^{2y}-e^x=c$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.