If y=y(x) satisfies the diffe ... | Differential Equations

JEE MAIN 2026

22-01-2026 S2

Question

If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y \mathrm{~d} y=(1+2 \sin y) \mathrm{d} x, x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$, then $2 \sin \alpha$ is equal to:

Select the correct option:

$3(\sqrt{2}-1)$

$2(\sqrt{2}-1)$

$2 \sqrt{2}-1$

$\sqrt{2}-1$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Hard

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