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: 7


$$ y=\frac{1}{2}(x+\frac{1}{2}\sin (2x))+\pi/4 .$$

Work Step by Step

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