Find the general solution of differential equation below : (cos x cos y + sin^2 x) dx − (sin x sin y + cos^2 y) dy = 0


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Question Number 58785 by naka3546 last updated on 30/Apr/19

$F i n d t h e g e n e r a l s o l u t i o n o f d i f f e r e n t i a l e q u a t i o n b e l o w :$ $(\cos x \cos y + \sin^{2} x) d x - (\sin x \sin y + \cos^{2} y) d y = 0$
	Answered by tanmay last updated on 30/Apr/19

	$c o s x c o s y d x - s i n x s i n y d y + {s i n}^{2} x d x - {c o s}^{2} y d y = 0$ $c o s y d (s i n x) + s i n x d (c o s y) + (\frac{1 - c o s 2 x}{2}) d x - (\frac{1 + c o s 2 y}{2}) d y = 0$ $d (s i n x c o s y) + \frac{d x}{2} - \frac{1}{2} c o s 2 x d x - \frac{d y}{2} - \frac{1}{2} c o s 2 y d y = 0$ $\int d (s i n x c o s y) + \frac{1}{2} \int d x - \frac{1}{2} \int c o s 2 x d x - \frac{1}{2} \int d y - \frac{1}{2} \int c o s 2 y d y = 0$ $s i n x c o s y + \frac{x}{2} - \frac{s i n 2 x}{4} - \frac{y}{2} - \frac{s i n 2 y}{4} = c$
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