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The solution of the differential equation [x cot y + log (cos x)] dy + [log sin y – y Tan x] dx = 0 is $(\sin y)^{A} (\cos x)^{B} = C$

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A = x

B = x

A = y

B = y

answer is A, D.

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Detailed Solution

$[xcot y + \log (\cos x)] dy + [\log (\sin y) - ytan x] dx$

$d [xlog (\sin y)] + d [ylog (\cos x)] = 0$

Integrate; $(\sin y)^{x} (\cos x)^{y} = c$

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