二阶线性微分方程的解法

The Solution to a Second Order Linear Differential Equation

本文讨论了二阶线性微分方程的解法.由于二阶线性微分方程解法的难易程度取决于其系数形式,为此讨论系数是常数和函数的二阶线性常微分方程.分别应用特征方程法和幂级数大意法求解这两种形式的二阶方程,并给出具体实例.

The solution to a second order linear differential equation is discussed in this paper. Because of solution to the second order linear differential equation depends on its coefficient form,second order linear ordinary differential equations which have constant and function coefficient are discussed in this paper. We use the methods of characteristic equation and a general meaning of the power series to solve these two forms of quadratic equation,respectively,and give concrete examples.