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

x = \frac{y^{2}}{3} + \frac{c}{y}

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x = \frac{y}{3} + \frac{c}{y}

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x^{2} = \frac{y^{2}}{3} + \frac{c}{y}

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x = \frac{3}{y^{2}} - \frac{c}{y}

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Solution

The correct option is A $x = \frac{y^{2}}{3} + \frac{c}{y}$
$y d x + x d y - y^{2} d y = 0$
$d (x y) = y^{2} d y$
Integrating both sides:
$x y = \frac{y^{3}}{3} + c$
$x = \frac{y^{2}}{3} + \frac{c}{y}$

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