Solve the following equation:
$y d x + (1 - y) x d y = 0$

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Solution

$y d x + (1 - y) x d y = 0$
$y d x = (y - 1) x d y$
$\int \frac{d x}{x} = \int \frac{y - 1}{y} d y$
$log x = \int (1 - \frac{1}{y}) d y$
$log x = y - 10 g y + c$
$log x + log y - y = c$
$log (x y) - y = c$

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