Exercise 101

Find the general solution to $\left[ \begin{smallmatrix} 1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3 \end{smallmatrix}\right] \vec{x}\,'' = \left[ \begin{smallmatrix} -3 & 0 & 0 \\ 2 & -4 & 0 \\ 0 & 6 & -3 \end{smallmatrix}\right] \vec{x} + \left[ \begin{smallmatrix} \cos(2t) \\ 0 \\ 0 \end{smallmatrix}\right]$.