一些特殊类型的变系数二阶线性微分方程解法的研究  

Some Methods for Solving Second Order Linear Differential Equations with Variable Coefficients

作　　者：文武[1] 

机构地区：[1]四川文理学院教务处,四川达州635000

出　　处：《大学数学》2016年第2期106-113,共8页College Mathematics

基　　金：四川省高等学校人文社会科学重点研究基地项目(NYJ20150604)

摘　　要：运用变量变换的方法将一些特殊类型的变系数二阶线性微分方程化为常系数二阶线性微分方程,或已知齐次方程的一个解来求出齐次方程的另一个线性无关解,从而达到按照常系数二阶线性微分方程的特殊方法和利用常数变易法来求方程的通解的目的,同时纠正了文献[3]的结论和例子2的错误.The variable transformation method , which is used for solving some special types of the second order linear differential equations with variable coefficients, and for calculating the another linearly independent solution through a known solution for the second order linear differential equations with constant coefficients,is discussed in this paper . Also, for the second order linear differential equations with constant coefficients, the method in this paper associated with variation of constants formula can be used for finding the general solution. In addition, some mistakes in literature [3] are corrected.

关 键 词：变系数二阶线性微分方程 特殊类型 变量变换 常数变易法 通解 

分 类 号：O175.1[理学—数学]