Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 8 - Mathematical Modeling With Differential Equations - 8.2 Separation Of Variables - Exercises Set 8.2 - Page 575: 3


$$y=c_1e^{-\sqrt{1+x^2} }-1$$

Work Step by Step

Given $$\frac{\sqrt{1+x^2}}{1+y}\frac{dy}{dx}=-x $$ Separate variables \begin{align*} \int \frac{dy}{1+y }&= \int \frac{-x}{\sqrt{1+x^2}} dx \\ \ln( y+1)&=-\sqrt{1+x^2}+c\\ y&= e^{[c-\sqrt{1+x^2}]}-1\\ &=c_1e^{-\sqrt{1+x^2} }-1 \end{align*}
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