Consider this second-order nonhomogeneous differential equation:

Which of these is a suitable form of a particular solution Y(t) of the nonhomogeneous differential equation if the method of undetermined coefficients is used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=A e^{-6 t}+B e^{9 t}+C t e^{-3 t}+D $
B) $ Y(t)=(A+B t)\left(e^{-6 t}+e^{9 t}+t e^{-3 t}+C\right. $
C) $ Y(t)=A e^{-6 t}+B e^{9 t}+(C t+
D) e^{-3 t}+E $
D) $ Y(t)=(A+B t) e^{-6 t}+(C+D t) e^{9 t}+(E+F t) e^{-3 t}+G $

Question

Consider this second-order nonhomogeneous differential equation:

Which of these is a suitable form of a particular solution Y(t) of the nonhomogeneous differential equation if the method of undetermined coefficients is used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=A e^{-6 t}+B e^{9 t}+C t e^{-3 t}+D $ 
B) $ Y(t)=(A+B t)\left(e^{-6 t}+e^{9 t}+t e^{-3 t}+C\right. $ 
C) $ Y(t)=A e^{-6 t}+B e^{9 t}+(C t+
D) e^{-3 t}+E $ 
D) $ Y(t)=(A+B t) e^{-6 t}+(C+D t) e^{9 t}+(E+F t) e^{-3 t}+G $

Quizplus · Accepted Answer

The Answer of Consider this second-order nonhomogeneous differential equation:

Which of these is a suitable form of a particular solution Y(t) of the nonhomogeneous differential equation if the method of undetermined coefficients is used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=A e^{-6 t}+B e^{9 t}+C t e^{-3 t}+D $ 
B) $ Y(t)=(A+B t)\left(e^{-6 t}+e^{9 t}+t e^{-3 t}+C\right. $ 
C) $ Y(t)=A e^{-6 t}+B e^{9 t}+(C t+
D) e^{-3 t}+E $ 
D) $ Y(t)=(A+B t) e^{-6 t}+(C+D t) e^{9 t}+(E+F t) e^{-3 t}+G $

Consider This Second-Order Nonhomogeneous Differential Equation: Which of These Y(t)=Ae−6t+Be9t+Cte−3t+D Y(t)=A e^{-6 t}+B e^{9 t}+C t e^{-3 t}+D Y(t)=Ae−6t+Be9t+Cte−3t+D

Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=A e^{-6 t}+B e^{9 t}+C t e^{-3 t}+D$