The solution of differential equation xdy−$$ydxx2+y2+$$$$tan$$−$$1$$⁡$$xy3(xdy+ydx)=0$$ is

Correct option is 2−12tan−1yx2+xy+c

Questions

$The solution of differential equation \frac{x d y - y d x}{x^{2} + y^{2}} + {(\tan^{- 1} (\frac{x}{y}))}^{3} (x d y + y d x) = 0 is$

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tan−1yx=ke−xy

−12tan−1yx2+xy+c

tan−1xy=kexy

−12tan−1yx2−xy+c

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detailed solution

Correct option is B

dtan−1⁡yxtan−1⁡yx3+d(xy)=0 Integrating both sides −12tan−1⁡yx2+xy=c

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The solution of differential equation xdy−ydxx2+y2+tan−1⁡xy3(xdy+ydx)=0 is

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$The solution of differential equation \frac{x d y - y d x}{x^{2} + y^{2}} + {(\tan^{- 1} (\frac{x}{y}))}^{3} (x d y + y d x) = 0 is$