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

A

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

B

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

C

$$\sqrt{2}-1$$

D

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