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: 27


$$ w=\tan(k\ln x+\pi/4) .$$

Work Step by Step

By separation of variables, we have $$\frac{dw}{1+w^2}=\frac{k}{x} dx$$ then by integration, we get $$ \tan^{-1}w=k\ln x+c \Longrightarrow w=\tan(k\ln x+c) .$$ Now, since $y(1)=1$, then $c=\pi/4$. So we have $$ w=\tan(k\ln x+\pi/4) .$$
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