线性常微分方程的保线性变换及其应用

研究了线性常微分方程的保线性变换，得到任意两个二阶线性常微分方程等价的条件，并用于求解一类二阶线性变系数齐次常微分方程．对数学物理方法教学中怎样通过适当的变换把给定的二阶线性变系数齐次常微分方程化为可解的方程给出了合理解释。

Linearity-preserving transformations of linear homogeneous ordinary differential equations and their application

Linearity-preserving transformations of linear ordinary differential equations are studied. Necessary and sufficient conditions are obtained, which allow two linear ordinary differential equations can be transformed from one to another. The conditions can be applied to solving the second-order linear homogeneous ordinary differential equations with variable coefficients. It also explained the reason how to find solution of a second-order linear homogeneous ordinary differential equations with variable coefficients through appropriate transformations in mathematical physics.