The solution of $y d x - x d y = 0$ is

y^{2} = c x

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y = c x^{3}

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y = c x

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x^{2} = c y

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Solution

The correct option is C $y = c x$
$y d x = x d y = 0$
$y d x = x d y$
$\int \frac{d x}{x} = \int \frac{d y}{y}$
$ln x = ln y + ln c$
$ln (\frac{x}{y}) = ln c \Rightarrow \frac{x}{y} = c$
$y = \frac{x}{c} = x c^{'}$
$y = x c^{'}$

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