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$The solution of the DE 2 x^{3} y d y + (1 - y^{2}) (x^{2} y^{2} + y^{2} - 1) d x = 0 is$

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x2y2=cx−11−y2

x2y2=cx+11+y2

xy=cx+1

xy=1+y2

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detailed solution

Correct option is A

At Div by 1−y222y1−y22dydx+y21−y21x=1x3 Put y21−y2=u⇒2y1−y22dydx=dudx⇒dudx+ux=1x3I.F.=∫e1 1xax=x Solu. is x2y2=(cx−1)1−y2

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The solution of the DE 2x3ydy+1−y2x2y2+y2−1dx=0 is

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$The solution of the DE 2 x^{3} y d y + (1 - y^{2}) (x^{2} y^{2} + y^{2} - 1) d x = 0 is$