Solution of differential equation $$x21x2+y2(xdy+ydx)+y2(xdy$$−$$ydx)=0$$ is

Correct option is 3tan−1xy+13yx3=c

Questions

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

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tan−1xy−12yx2=c

tan−1xy+12yx2=c

tan−1xy+13yx3=c

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detailed solution

Correct option is C

Given differential equation is x21x2+y2(xdy+ydx)+y2(xdy−ydx)=0⇒x41+x2y2(xdy+ydx)+y2(xdy−ydx)=0⇒11+x2y2(xdy+ydx)+y2x2xdy−ydxx2=0⇒dtan−1⁡xy+13dyx3=0⇒tan−1⁡(xy)+13yx3=c

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Solution of differential equation x21x2+y2(xdy+ydx)+y2(xdy−ydx)=0 is

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