JEE Math Practice Question

Let $$y=y(x)$$ be the solution curve of the differential equation $$\sec y \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x \sin y=x^3 \cos y, y(1)=0$$. Then $$y(\sqrt{3})$$ is equal to:

1. A.$$\frac{\pi}{6}$$
2. B.$$\frac{\pi}{12}$$
3. C.$$\frac{\pi}{3}$$
4. D.$$\frac{\pi}{4}$$