二阶常系数齐次线性微分方程边值问题的解的相似结构

The Similar Structure of Solution of Second-order Linear Homogeneous Differential Equation with Constant Coefficients on the Boundary Value Problem

通过对常系数齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式,说明了该类微分方程的解具有类似于实数可表为连分式、图形具有相似性的所谓式相似性质,指出了解式的相似性质的研究有利于进一步分析解的内在规律,解决相应的应用问题,方便编制相应的分析软件。它是微分方程理论的新发展。

Through reducing the analysis expression of boundary value problem on a class of second-order linear homogeneous differential equation with constant coefficients,the paper presents the solution's formal similarity.This similar structure reflects that the class equation can be obtained by the product of several fractions and the graphs have similarity as well.The character resembles that of the real number.The result obtained is beneficial to understand the inherent laws of relevant engineering science and design of the practical analysis software.Furthermore,it promotes the progress of equation theory