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) $y(t) =C_{1} e^{3 t}(\sin (4 t) +\cos (4 t) ) +C_{2}$
B) $y(t) =C_{1} e^{4 t}\left(\sin (3 t) +C_{2} e^{4 t}(\cos (3 t) \right.$
C) $y(t) =C_{1} e^{4 t}(\sin (3 t) +\cos (3 t) ) +C_{2}$
D) $y(t) =C_{1} e^{3 t}\left(\sin (4 t) +C_{2} e^{3 t}(\cos (4 t) \right.$