Special-series solution of the first-order linear vector differential equation

Details Special-series solution of the first-order linear vector differential equation Special-series solution of the first-order linear vector differential equation

2005-03-08

arxiv.org/abs/math/0503158v1

Mathematics

Classical Analysis and ODEs

14 pages, no figures, submitted to J.Differential Equations

Scientific paper

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.

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