Which of These Is the General Solution of the Second-Order $y(t)=C_{1} e^{\frac{1}{2} t}+C_{2} t e^{\frac{1}{2} t}+\left(A t^{2}+B t+C\right) e^{\frac{1}{2} t}+D$

Multiple Choice

Which of these is the general solution of the second-order nonhomogeneous differential equation
and all capital letters are arbitrary real constants.

A) $y(t) =C_{1} e^{\frac{1}{2} t}+C_{2} t e^{\frac{1}{2} t}+\left(A t^{2}+B t+C\right) e^{\frac{1}{2} t}+D$
B) $y(t) =C_{1} e^{\frac{1}{2} t}+C_{2} t e^{\frac{1}{2} t}+A e^{\frac{1}{2} t}+B$
C) $y(t) =e^{\frac{1}{2} t}\left(C_{1}+C_{2} t\right) +(A t+B) e^{\frac{1}{2} t}+C$
D) $y(t) =e^{-\frac{1}{2} t}\left(C_{1}+C_{2} t\right) +\left(A t^{2}+B t+C\right) e^{\frac{1}{2} t}+D$
E) $y(t) =e^{-\frac{1}{2} t}\left(C_{1}+C_{2} t\right) +A e^{\frac{1}{2} t}+B$