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MCQMediumJEE Main 2026 · 22 January, Shift 2Separation of Variables

Mathematics Question from JEE Main 2026 · 22 January, Shift 2

If y=y(x)y=y(x) satisfies the differential equation 16x 9+x (4+9+x)cos⁡y dy=(1+2sin⁡y) dx,x>016\sqrt{x}\,\sqrt{9+\sqrt{x}}\,\left(4+\sqrt{9+\sqrt{x}}\right)\cos y\,dy=(1+2\sin y)\,dx,\quad x>0 and y(256)=π2,y(49)=α,y(256)=\frac{\pi}{2},\quad y(49)=\alpha, then 2sin⁡α2\sin\alpha is equal to

  • A

    2(2−1)2(\sqrt{2}-1)

  • B

    (2−1)(\sqrt{2}-1)

  • C

    22−12\sqrt{2}-1

  • D

    3(2−1)3(\sqrt{2}-1)

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