.$$  Therefore, the general solution of the system for the first vector is $${\overrightarrow{\bf e}_0}(u) := \sum_{\ell=0}^{k}\overrightarrow{A_\ell}\ e^{a_\ell u}\cos(b_\ell\ u) +\overrightarrow{B_\ell}\ e^{a_\ell u}