A solution of the differential equation $(x^{2} y^{2} - 1) d y + 2 x y^{3} d x = 0$ is:

1 + x^{2} y^{2} = c x

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1 + x^{2} y^{2} = c y

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y = 0

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y = - \frac{1}{x^{2}}

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Solution

The correct option is A $1 + x^{2} y^{2} = c y$
Given differential equation is, $(x^{2} y^{2} - 1) d y + 2 x y^{3} d x = 0$
$x^{2} y^{2} d y + 2 x y^{3} d x = d y$
$x^{2} d y + 2 x y d x = \frac{d y}{y^{2}}$
$d (x^{2} y) = \frac{d y}{y^{2}}$
Taking integration, we get
$\Rightarrow x^{2} y = - \frac{1}{y} + c$
$\Rightarrow x^{2} y^{2} + 1 = c y$

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C

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