Consider This Second-Order Nonhomogeneous Differential Equation:

Which of the Following

Multiple Choice

Consider this second-order nonhomogeneous differential equation:

Which of the following is the form of the solution of the corresponding homogeneous differential equation? Here, C₁ and C₂ are arbitrary real constants.

A) $y(t) =C_{1} e^{-3 t}+C_{2} e^{7 t}$
B) $y(t) =C_{1} e^{-3 t}+C_{2} t e^{-3 t}$
C) $y(t) =C_{1} e^{3 t}+C_{2} t e^{3 t}$
D) $y(t) =C_{1} e^{3 t}+C_{2} e^{-7 t}$
E) $y(t) =C_{1} e^{-7 t}+C_{2} t e^{-7 t}$