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