线性微分方程组解的结构的注记

A Note on the Structure of Solutions to Linear Differential Equation Systems

摘要: 一般线性微分方程组解的结构都是从齐次微分方程组的基解矩阵出发得到相应非齐次微分方程组的基本解组。本文主要讨论了从非齐次微分方程的基本解组如何构造对应齐次微分方程的基本解组。

Abstract: Under the conventional framework of linear differential equation systems, the structure of solutions is typically derived from the fundamental solution matrix of the homogeneous system to obtain the general solution of the corresponding nonhomogeneous system. This paper, however, focuses on the reverse direction: constructing the fundamental solution set of the homogeneous equation from a known fundamental solution set of the nonhomogeneous system.