The solution of $(5 x^{2} - y) d x + x d y = 0$ is:

5 x^{2} + 3 x y = c

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y + 5 x^{2} = c x

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\frac{y}{x} + 5 x^{2} = c x

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\frac{5}{3} x^{3} + x y = c

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Solution

The correct option is A $y + 5 x^{2} = c x$
$\Rightarrow 5 x^{2} - y + x \frac{d y}{d x} = 0$

$\Rightarrow \frac{1}{x} \frac{d y}{d x} - \frac{y}{x^{2}} = - 5$

$\Rightarrow \frac{d}{d x} (^{y} /_{x}) = - 5$

$\Rightarrow \int d (^{y} /_{x}) = \int - 5 d x + c$

$\Rightarrow \frac{y}{x} = - 5 x + c$

$\Rightarrow y + 5 x^{2} = c x$

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$- x^{3} - 125$

$\sqrt{5} x^{2} + x + \sqrt{5} = 0$

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