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Differential Equations question

2024 · 31 Jan · Shift 1 · Q46

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JEE Main
Mathematics
Differential Equations
2024 · 31 Jan · Shift 1 · Q46

Differential Equations question

2024 · 31 Jan · Shift 1 · Q46

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The solution curve of the differential equation

y \frac{d x}{d y}=x\left(\log _e x-\log _e y+1\right), x\gt 0, y\gt 0

passing through the point

(e, 1)

is

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

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