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

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y=xcot(c-x)

9cos-1(y/x)=c-x

y=xtan(c-x)

y2x2=xtan(c-x)

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detailed solution

Correct option is C

xdy−ydxx2+y2=−dx⇒∫dTan−1⁡(y/x)=−∫dx⇒Tan−1⁡(y/x)=-x+c⇒y=xtan(c−x)

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The solution of the differential equation xx2+y2dy=yx2+y2−1dx is

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