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Question

The solution curve of the differential equation $y \frac{d x}{d y}=x\left(\log _e x-\log _e y+1\right), x>0, y>0$ passing through the point $(e, 1)$ is

$\left|\log _e \frac{y}{x}\right|=y^2$
$\left|\log _e \frac{y}{x}\right|=x$
$\left|\log _e \frac{x}{y}\right|=y$
$2\left|\log _e \frac{x}{y}\right|=y+1$

Solution

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