Solution of systems of linear ordinary differential equations with periodic coefficients

An analysis technique is presented to provide an essentially explicit solution for a system of n simultaneous first-order linear differential equations with periodic coefficients. This representation of a periodic variable-parameter linear system of arbitrary finite order is chosen for its theoretical and practical advantages over the classical nth order linear differential equation. Emphasis is placed on natural mode solutions of a homogeneous set of equations. The characteristic exponents for these solutions are determined from a polynomial equation the coefficients of which are linear combinations of n — 1 convergent infinite-order determinants. Approximate calculation of these determinants is feasible for problems of moderate order.