巧学妙用常系数齐次线性微分方程——一道赛题的另一种解法

Skillful Application of Homogeneous Constant Coefficients Linear Differential Equation

对一道数学竞赛题,介绍微分方程解法,通过对参数β取值的分类讨论,将原命题等价转化成一阶和二阶常系数齐次线性微分方程的求解问题,能够直观地给出证明.

This paper uses differential equation method to solve a contest problem. By discussing the value of parameter ＂, the original problem is transformed into a first or second order homogeneous linear differ-ential equation with constant coefficients, which can be solved easily.