Find the particular solution for the differential equation $\frac{dy}{dx}=\frac{2x^3}{3y}$ at $y(0)=3.$

Choose the correct answer below.

A$.y=\frac{1}{3}{x}^{4}3$

B$.y=3x^{3}3$

C$.y^2=3x^{3}9$

D$.y^2=\frac{1}{3}{x}^{4}9$