Match the following differential equations with their solutions. The symbols $A,B,C$ in the solutions stand for arbitrary constants. You must get all of the answers correct to receive credit.

$\frac{d^{2}y}{d{x}^2}+9y=0$

$\frac{dy}{dx}=\frac{-2xy}{x^2-3y^2}$

$\frac{d^{2}y}{d{x}^2}+16\frac{dy}{dx}+64y=0$

$\frac{dy}{dx}=6xy$

$\frac{dy}{dx}+24x^{2}y=24x^2$

A$.y=A{e}^{3x^2}$

B$.y=A{e}^{-8x}+Bx{e}^{-8x}$

C$.y=$Acos$(3x)+$Bsin$(3x)$

D$.y=C{e}^{-8x^3}+1$

E$.3y{x}^2-3y^3=C$