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: 44


$$ y=\frac{1}{(3/2)+\cos x} .$$

Work Step by Step

By separation of variables, we have $$y^{-2}dy=\sin x dx $$ then by integration, we get $$ -y^{-1}=-\cos x+c .$$ Now, since $y(\pi)=2$, then $c=-3/2$. So the general solution is given by $$ y=\frac{1}{(3/2)+\cos x} .$$
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