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MCQMediumJEE Main 2025 · 23 January, Shift 2Homogeneous Differential Equations

Mathematics Question from JEE Main 2025 · 23 January, Shift 2

Let x=x(y)x = x(y) be the solution of the differential equation:

y=(x−ydxdy)sin⁡(xy), y>0 and x(1)=π2.y = \left( x - y \frac{dx}{dy} \right) \sin\left( \frac{x}{y} \right), \, y > 0 \, \text{and} \, x(1) = \frac{\pi}{2}.

Then cos⁡(x(2))\cos(x(2)) is equal to:

  • A

    1−2(log⁡2)21 - 2(\log 2)^2

  • B

    2(log⁡2)2−12(\log 2)^2 - 1

  • C

    2(log⁡2)−12(\log 2) - 1

  • D

    1−2(log⁡2)1 - 2(\log 2)

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