微分算子法在处理线性微分方程通解理论中的应用

Application of Differential Operator Method in Dealing with Theory of General Solution of Linear Differential Equations

在已有文献的一些理论基础上,以微分算子及多项式算子对经典的线性微分方程通解理论进行了更为系统的总结和发展,得到了一些关于线性微分方程及其方程组通解理论的新成果。该方法具有较为明显的系统性和连贯性,从而对学习和研究线性微分方程通解理论具有一定的指导性和启发性。

Based on some theories from the existing literature, this p aper made a more systematicalsummary and development on the classical theory of general solutions of linear differential equations by themethods of differential operator and polynomial operator, and got new results on the general solutions of linear differential equations and its equations system. The methods are significantly systematic and coherentand thus able to be instructive in the learning and studying the general solution theory of linear differentialequations.