Solve $$dydx=x3y3$$−xy

Correct option is 2x2+1+cex2y2=1

Questions

$Solve \frac{d y}{d x} = x^{3} y^{3} - x y$

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y2+1+cey2=1

x2+1+cex2y2=1

y2+1+cey2=x

x+1+cey2x2=1

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detailed solution

Correct option is B

G.E dydx+xy=x3y3⇒1y3dydx+xy2=x3 Put 1y2=z⇒dzdx−2xz=−2x3;I.F=e−x2 General solution ze−x2∫−2x3e−x2dx Put x2=t⇒ze−x2=−∫te−tdt ⇒1y2e−x2=x2e−x2+e−x2+c⇒x2+1+cex2y2=1

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Solve dydx=x3y3−xy

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$Solve \frac{d y}{d x} = x^{3} y^{3} - x y$