The equation of the curve passing through the point (0, \pi) and satisfying the differential equation y \dx= (x+y^3 \cos y) d y is [AP EAPCET 23 May 2025 S2]

Correct Answer is : x=y2siny+2ycos2y2

x=y^2 \sin y+2 y \cos ^2 \frac{y}{2}

x=y^2 \sin y+y \cos ^2 \frac{y}{2}