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: 8


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

Work Step by Step

By separation of variables, we have $$ \sec^2ydy= dx $$ then by integration, we get $$ \tan y=x+c .$$ Now, since $y(0)=\pi/4$, then $c=1$. So the general solution is given by $$ y=\tan^{-1}(x+1) .$$
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