Series solution to the general linear time varying system

The homogeneous solution (i.e., state transition matrix) to the general linear time varying system is shown to be a matrix power series generated by a time-varying matrix-differential operator operating recursively and noncommutatively on the identity matrix. The particular solution is shown to be a similar series generated by the same matrix operator operating recursively and noncommutatively on the time-varying vector-forcing function. The reduction to the time-invariant case is direct.