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

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tanxy=logcx

xy=tanlogcx

x+y=xytanxy+c

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Correct option is C

Given equation is 1−xy+x2y2dx=x2dy⇒1+x2y2dx=x(ydx+xdy)⇒ydx+xdy1+x2y2=dxx⇒d(xy)1+(xy)2=dxx Integrating on both sides ⇒∫d(xy)1+(xy)2=∫dxx⇒tan−1⁡(xy)=log⁡|x|+log⁡|C|⇒tan−1⁡(xy)=log⁡|xC|⇒(xy)=tan⁡(log⁡|xC|)

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The solution of differential equation 1−xy+x2y2dx=x2dy is

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