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) $y(t) =C_{1} \sin (5 t) +C_{2} \cos (5 t)$
B) $y(t) =C_{1} \sin (25 t) +C_{2} \cos (25 t)$
C) $y(t) =C_{1}+C_{2} e^{-5 t}$
D) $y(t) =C_{1} e^{-5 t}+C_{2} e^{5 t}$