Given, y xdydx=0 dydx=yx dyy=dxx integrating on both sides, we get, ∫dyy=∫dxx log y =log x+c ...

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Variable Separable Method

y-xdydx=0

Question

$y - x \frac{d y}{d x} = 0$

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Solution

Given,

$y - x \frac{d y}{d x} = 0$

$\frac{d y}{d x} = \frac{y}{x}$

$\frac{d y}{y} = \frac{d x}{x}$

integrating on both sides, we get,

$\int \frac{d y}{y} = \int \frac{d x}{x}$

$log y = log x + c$

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