Answer
$e^y - y = 2x + \sin(x) + C$
Work Step by Step
$(e^y-1)y'=2+\cos(x) \quad \rightarrow \quad \displaystyle \frac{dy}{dx}(e^y-y)=2+\cos(x)$
$\displaystyle \int (e^y-1)dy = \int[2+\cos(x)]dx$
$e^y-y=2x+\sin(x)+C$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 9 - Differential Equations - 9.3 Separable Equations - 9.3 Exercises - Page 645: 5
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