What Is the General Solution of the Third-Order Homogeneous Differential $y=C_{1}+C_{2} e^{2 t} \cos \left(\frac{\sqrt{32}}{2} t\right)+C_{3} e^{2 t} \cos \left(\frac{\sqrt{32}}{2} t\right)$

Multiple Choice

What is the general solution of the third-order homogeneous differential equation

A) $y=C_{1}+C_{2} e^{2 t} \cos \left(\frac{\sqrt{32}}{2} t\right) +C_{3} e^{2 t} \cos \left(\frac{\sqrt{32}}{2} t\right)$
B) $y=C_{1}+C_{2} e^{-2 t} \cos \left(\frac{\sqrt{32}}{2} t\right) +C_{3} e^{-2 t} \cos \left(\frac{\sqrt{32}}{2} t\right)$
C) $y=C_{1}+C_{2} e^{\frac{4-\sqrt{32}}{2} t}+C_{3} e^{\frac{4+\sqrt{32}}{2} t}$
D) $y=C_{1}+C_{2} e^{\frac{-4-\sqrt{32}}{2}}+C_{3} e^{\frac{-4+\sqrt{32}}{2}}$