变系数二阶线性微分方程的一个可解定理

A Solvable Theorem to Variable Coefficient Second Order Linear Differential Equation

研究在理论上和应用上占有重要地位的二阶线性微分方程的解法 ,给出了二阶变系数线性微分方程经自变量化为二阶常系数线性微分方程的充要条件 ,推广了一些经典的和近代的可解结果 。

In this paper,the solvable of second order linear differential equation which is important in theory and practice is studied. The necessary and sufficient condition that variable coefficient second order linear differential eqcation transforms into constant coefficient linear differential equation via independent variable is given. Some classical and modern solvable results are extended. The predecessor′s one-sidedness of some results is repaired.