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$The solution of the D.E (2 y + x y^{3}) d x + (x + x^{2} y^{2}) d y = 0 is$

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x2y+x3y33=C

xy2+x3y33=C

x2y+x4y44=C

x2y-x3y33=C

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detailed solution

Correct option is A

(2ydx+xdy)+xy3dx+x2y2dy=0 Multiplying by x2xydx+x2dy+x2y3dx+x3y2dy=02xy+x2dydx+x2y3+x3y2dydx=0→dx2y+13dx3y3=0→∫dx2y+13∫dx3y3=0→x2y+x3y33=C

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The solution of the D.E 2y+xy3dx+x+x2y2dy=0 is

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$The solution of the D.E (2 y + x y^{3}) d x + (x + x^{2} y^{2}) d y = 0 is$