  A special series is introduced in this paper to yield solution of the
first-order linear vector differential equation. It is proved that if the
differential equation satisfied by the first term of this series can be solved
exactly, then other terms can be determined by the method of variation of
parameters. We point out that the special series will be the solution of the
first-order linear vector differential equation if the infinite special series
converges. An illustrative example has been given to outline the procedure of
our method.
