The solution of $$sin$$⁡$$xy(ydx$$−$$xdy)=xy3(xdy+ydx)$$ is

Correct option is 3xy22+cosxy+c=0

Questions

$The solution of \sin (\frac{x}{y}) (y d x - x d y) = x y^{3} (x d y + y d x) is$

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xy2+sinxy+c=0

xy22+sinxy+c=0

xy22+cosxy+c=0

xy+tanxy+c=0

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detailed solution

Correct option is C

Given differential equation issin⁡xy(ydx−xdy)=xy3(xdy+ydx)⇒sin⁡xyydx−xdyy2=xy(xdy+ydx)⇒d−cos⁡xy=12d(xy)2⇒−cos⁡xy=12(xy)2⇒−cos⁡xy=12(xy)2+c⇒xy22+cosxy+c=0

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The solution of sin⁡xy(ydx−xdy)=xy3(xdy+ydx) is

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$The solution of \sin (\frac{x}{y}) (y d x - x d y) = x y^{3} (x d y + y d x) is$