What Is the General Solution of the Fifth-Order Homogeneous Differential $y=C_{1}+C_{2} t+C_{3} t^{2}+C_{4} e^{3 t}+C_{5} t e^{3 t}$

Multiple Choice

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

A) $y=C_{1}+C_{2} t+C_{3} t^{2}+C_{4} e^{3 t}+C_{5} t e^{3 t}$
B) $y=C_{1}+C_{2} t+C_{3} t^{2}+C_{4} e^{-3 t}+C_{5} t e^{-3 t}$
C) $y=C_{1}+C_{2} t+C_{3} e^{3 t}+C_{4} t e^{3 t}+C_{5} t^{2} e^{3 t}$
D) $y=C_{1}+C_{2} t+C_{3} e^{-3 t}+C_{4} t e^{-3 t}+C_{5} t^{2} e^{-3 t}$