Which of These Is the General Solution of the Second-Order $y(t)=C_{1} e^{-4 t}+C_{2} e^{\frac{t}{4}}+A e^{-4 t}+B e^{4 t}+C e^{5 t}$

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