Answer
$2y+\cos y = x + \sin x + C$
Work Step by Step
Multiplying both sides by $(2-\sin y) dx$ gives $$(2-\sin y) dy = (1+\cos x) dx$$ Integrating both sides gives
$$2y+\cos y = x + \sin x + C$$
Elementary Differential Equations and Boundary Value Problems 9th Edition
by Boyce, William E.; DiPrima, Richard C.
Published by
Wiley
ISBN 10:
0-47038-334-8
ISBN 13:
978-0-47038-334-6
Chapter 2 - First Order Differential Equations - 2.9 First Order Difference Equations - Problems - Page 132: 2
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