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

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exyxy−1+logy=c

ex/yx/y−1+logy=c

ey/xy/x−1+logx=c

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Correct option is B

The given equation can be re written as ⇒y2−x2ex/ydy=−xyex/ydx⇒dxdy=x2ex/y−y2xyex/y=xy-1xyex/y Put x=vy then ⇒dxdy=v+ydvdy⇒v+ydvdy=v−1vev⇒∫vevdv=−∫dyy⇒ev(v−1)=−ln⁡|y|+c⇒ex/yxy−1+ln⁡y=c

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The solution of the differential equation y2dy=xxdy−ydxex/y is

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