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$The solution of the differential y (xy + 2 x^{2} y^{2}) dx + x (xy - x^{2} y^{2}) dy = 0 is given by$

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2logx-logy-1xy=c

2logy-logx-1xy=c

2logx+logy+1xy=c

2logy+logx+1xy=c

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detailed solution

Correct option is A

xy(ydx+xdy)+x2y2(2ydx-xdy)=0÷by x3y3⇒∫d(xy)x2y2+∫2xdx−1ydy=∫0⇒−1xy+2log⁡|x|−log⁡|y|=c

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The solution of the differential yxy+2x2y2dx+xxy−x2y2dy=0 is given by

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$The solution of the differential y (xy + 2 x^{2} y^{2}) dx + x (xy - x^{2} y^{2}) dy = 0 is given by$