The solution of the differential equation $x d x + y d y = x^{2} y d y - y^{2} x d x$ is

x^{2} - 1 = C (1 + y^{2})

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x^{2} + 1 = C (1 - y^{2})

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x^{3} - 1 = C (1 + y^{3})

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x^{3} + 1 = C (1 - y^{3})

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Solution

The correct option is A $x^{2} - 1 = C (1 + y^{2})$
$x d x + y d y = x^{2} y d y - y^{2} x d x$
$y d y (x^{2} - 1) = x d x (1 + y^{2})$
$\int \frac{y}{1 + y^{2}} d y - \int \frac{x}{x^{2} - 1} d x$
$\Rightarrow x^{2} - 1 = C (1 + y^{2})$

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