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