A free oscillator whose equation is \begin{gather*} x ̈ + 2x ̇ + 2x = 0 \end{gather*} is intervened with a forcing function \begin{gather*} g(t) = 4 \cos(t) + 2 \sin(t) \end{gather*}
I know the equation of the forced oscillator can be: \begin{gather*} x ̈ + 2x ̇ + 2x = 0, \end{gather*} \begin{gather*} x ̈ + 2x ̇ + 2x = 4 \cos(t) + 2 \sin(t), \end{gather*} \begin{gather*} x ̈ + 2x ̇ + 2x = 2 \cos(t) + \sin(t) \end{gather*} but I don't have any idea why