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 to be used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=\left(e^{-6 t}+e^{-2 t}\right) \cdot(A t+
B) $
B) $ Y(t)=A t+B $
C) $ Y(t)=A t $
D) $ Y(t)=A t+e^{-6 t}+e^{-2 t} $

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 to be used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=\left(e^{-6 t}+e^{-2 t}\right) \cdot(A t+
B) $ 
B) $ Y(t)=A t+B $ 
C) $ Y(t)=A t $ 
D) $ Y(t)=A t+e^{-6 t}+e^{-2 t} $

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 to be used? Here, all capital letters represent arbitrary real constants.
A) $ Y(t)=\left(e^{-6 t}+e^{-2 t}\right) \cdot(A t+
B) $ 
B) $ Y(t)=A t+B $ 
C) $ Y(t)=A t $ 
D) $ Y(t)=A t+e^{-6 t}+e^{-2 t} $

Consider This Second-Order Nonhomogeneous Differential Equation: Which of These Y(t)=(e−6t+e−2t)⋅(At+B) Y(t)=\left(e^{-6 t}+e^{-2 t}\right) \cdot(A t+B) Y(t)=(e−6t+e−2t)⋅(At+B)

Consider This Second-Order Nonhomogeneous Differential Equation:

Which of These $Y(t)=\left(e^{-6 t}+e^{-2 t}\right) \cdot(A t+B)$