Find the particular solution for the initial value problem $$2 \sin(y^2) dx + xy \cos(y^2)dy = 0$$, if $$y(2) = \sqrt{ \left(\frac{\pi}{2}\right)}$$

A

$$x^4 \sin (y^3) = 28$$

B

$$x^3 \sin (y^2) = 8$$

C

$$x^4 = 16$$

D

$$x^4 \sin (y^2) = 16$$