Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 505: 27


$y= \sin ^{-1}(\frac{x^{2}}{2}+C) $

Work Step by Step

$\frac{dy}{dx}=x\sec y$ Separating the variables, we have $\frac{dy}{\sec y}=xdx$ or $\cos y \, dy=xdx$ Integrating both sides, we get $\int\cos y\,dy=\int xdx$ $\sin y=\frac{x^{2}}{2}+C$ or $y=\sin^{-1}(\frac{x^{2}}{2}+C)$ where C is an arbitrary constant.
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