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MCQMediumJEE Main 2024 · 31 January, Shift 1Separation of Variables

Mathematics Question from JEE Main 2024 · 31 January, Shift 1

The solution curve of the differential equation: ydxdy=x[(ln⁡(x))−(ln⁡(y))+1]y \frac{dx}{dy} = x \left[(\ln(x)) - (\ln(y)) + 1\right], with x>0x > 0, y>0y > 0, passing through the point (e,1)(e, 1)

  • A

    ∣ln⁡(yx)∣=x\left|\ln\left(\frac{y}{x}\right)\right| = x

  • B

    ∣ln⁡(yx)∣=y2\left|\ln\left(\frac{y}{x}\right)\right| = y^2

  • C

    ∣ln⁡(xy)∣=y\left|\ln\left(\frac{x}{y}\right)\right| = y

  • D

    2∣ln⁡(xy)∣=y+12\left|\ln\left(\frac{x}{y}\right)\right| = y + 1

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