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$The solution of differential equation x d y (y^{2} e^{x y} + e^{x / y}) = y d x (e^{x / y} - y^{2} e^{x y}), is$

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xy=logex+λ

x2/y=logex/y+λ

xy=logex/y+λ

xy2=logex/y+λ

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detailed solution

Correct option is C

xdyy2exy+ex/y=ydxex/y−y2exy⇒ex/y(xdy−ydx)=−exy(xdy+ydx)y2⇒ex/yydx+xdyy2=exy(xdy+ydx)⇒∫ex/ydxy=∫exyd(xy)⇒ex/y+c=exy⇒xy=log⁡ex/y+c

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The solution of differential equation xdyy2exy+ex/y=ydxex/y−y2exy , is

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$The solution of differential equation x d y (y^{2} e^{x y} + e^{x / y}) = y d x (e^{x / y} - y^{2} e^{x y}), is$