Calculus (3rd Edition)

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

Chapter 10 - Introduction to Differential Equations - Chapter Review Exercises - Page 526: 32



Work Step by Step

Given $$y'= \sec y$$ Then \begin{align*} \frac{dy}{dx}&= \sec y\\ \frac{1}{\sec y} dy&=dx\\ \int \cos y dy&=\int dx\\ \sin y&=x+C \end{align*} Since $y(0)=0$, then $C=0$, and hence $$ \sin y=x\ \ \Rightarrow \ \ y=\sin^{-1}x$$
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