## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 10 - Introduction to Differential Equations - Chapter Review Exercises - Page 526: 7

#### Answer

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

#### 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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