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{9}{2} t}+C_{2} t e^{-\frac{9}{2} t}+\mathrm{A} t^{2} $
B) $ y(t)=e^{-\frac{9}{2} t}\left(A t^{2}+B t+C\right)+C_{1} $
C) $ y(t)=e^{\frac{9}{2} t}\left(t+C_{1}\right)+A t^{2}+B t+C $
D) $ y(t)=e^{-\frac{9}{2} t}\left(C_{1}+C_{2} t\right)+A t^{2}+B t+C $
E) $ y(t)=C_{1} e^{\frac{9}{2} t}+C_{2} t e^{\frac{9}{2} t}+A t^{2}+B t $

Question

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{9}{2} t}+C_{2} t e^{-\frac{9}{2} t}+\mathrm{A} t^{2} $ 
B) $ y(t)=e^{-\frac{9}{2} t}\left(A t^{2}+B t+C\right)+C_{1} $ 
C) $ y(t)=e^{\frac{9}{2} t}\left(t+C_{1}\right)+A t^{2}+B t+C $ 
D) $ y(t)=e^{-\frac{9}{2} t}\left(C_{1}+C_{2} t\right)+A t^{2}+B t+C $ 
E) $ y(t)=C_{1} e^{\frac{9}{2} t}+C_{2} t e^{\frac{9}{2} t}+A t^{2}+B t $

Quizplus · Accepted Answer

The Answer of 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{9}{2} t}+C_{2} t e^{-\frac{9}{2} t}+\mathrm{A} t^{2} $ 
B) $ y(t)=e^{-\frac{9}{2} t}\left(A t^{2}+B t+C\right)+C_{1} $ 
C) $ y(t)=e^{\frac{9}{2} t}\left(t+C_{1}\right)+A t^{2}+B t+C $ 
D) $ y(t)=e^{-\frac{9}{2} t}\left(C_{1}+C_{2} t\right)+A t^{2}+B t+C $ 
E) $ y(t)=C_{1} e^{\frac{9}{2} t}+C_{2} t e^{\frac{9}{2} t}+A t^{2}+B t $

Which of These Is the General Solution of the Second-Order y(t)=C1e−92t+C2te−92t+At2 y(t)=C_{1} e^{-\frac{9}{2} t}+C_{2} t e^{-\frac{9}{2} t}+\mathrm{A} t^{2} y(t)=C1​e−29​t+C2​te−29​t+At2

Which of These Is the General Solution of the Second-Order $y(t)=C_{1} e^{-\frac{9}{2} t}+C_{2} t e^{-\frac{9}{2} t}+\mathrm{A} t^{2}$