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: 42


$$ y= \tan(\sin^{-1}x).$$

Work Step by Step

By separation of variables, we have $$\frac{dy}{y^2+1}=\frac{dx}{\sqrt{1-x^2}} $$ then by integration, we get $$\tan^{-1}y=\sin^{-1}x+c\Longrightarrow y= \tan(\sin^{-1}x+c).$$ Now, since $y(0)=0$, then $c=0$. So the general solution is given by $$ y= \tan(\sin^{-1}x).$$
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