If y=y(x) satisfies the differential equation 16(\sqrt{x+9 {\sqrt{x}})(4+\sqrt{9+{\sqrt{x}}) \cos y d y=(1+2 \sin y) \dx, x>0 and y(256)=\frac{\pi}{2}, y(49)=\alpha, then 2 \sin \alpha is equal to : [22 Jan 2026 Shift 2]

Differential Equations Part 3

Section: Mathematics

Question : 6 of 34

Marks: +1, -0

If y=y(x) satisfies the differential equation 16(√x+9√x)(4+√9+√x)‌cos‌y‌d‌y=(1+2sin‌y)‌dx,x>0 and y(256)=‌

,y(49)=α, then 2sin‌α is equal to :

[22 Jan 2026 Shift 2]

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