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# find the general solution of the differential equation

$cosec ^2 (x)\cot ydx+cosec ^2 (y)\cot xdy=0$

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$cosec ^2 (x)\cot ydx+cosec ^2 (y)\cot xdy=0$

$\frac{cosec^2 x}{\cot x}dx = -\frac{cosec^2 y}{\cot y}dy$

$\\ \Rightarrow \int \tan x dx = -\int \tan ydy$

$\\ \Rightarrow ln|\sec x| = -ln|\sec y|$

$\\ \Rightarrow ln|(\sec x)(\sec y)| = 0 \\ \Rightarrow (\sec x)(\sec y) = 1 \\ \Rightarrow \cos x\times\cos y = 1$???????

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