Which of the Following Are Solutions to the Homogeneous Second-Order $y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t}$

Multiple Choice

Which of the following are solutions to the homogeneous second-order differential equation ?
Select all that apply.

A) $y_{1}=e^{-\frac{3}{2} t}+e^{\frac{3}{2} t}$
B) $y_{2}=-6 t e^{\frac{3}{2} t}+8$
C) $y_{3}=C_{1} e^{-\frac{3}{2} t}+C_{2} t e^{-\frac{3}{2} t}$ , where $C_{1}$ and $C_{2}$ are arbitrary real constants
D) $y_{4}=8 e^{\frac{3}{2} t}$
E) $y_{5}=C e^{\frac{3}{2} t}+10 t e^{\frac{3}{2} t}$
F) $y_{6}=2 e^{\frac{3}{2} t}+8 t e^{\frac{3}{2} t}+8$ 42_00