Consider This Second-Order Nonhomogeneous Differential Equation:

Which of the Following

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) $y(t) =e^{2 t}+e^{5 t}+C_{1}$
B) $y(t) =C_{1}\left(e^{2 t}+e^{-5 t}\right) +C_{2}$
C) $y(t) =C_{1} e^{-2 t}+C_{2} e^{-5 t}$
D) $y(t) =C_{1} e^{-2 t}+C_{2} e^{5 t}$
E) $y(t) =C_{1}\left(e^{-2 t}+e^{-5 t}\right) +C_{2}$