二阶变系数线性微分方程的变量变换法  

Variable Transformation Method of Second Order Linear Differential Equations with Variable Coefficients

作　　者：王慧 叶永升 WANG Hui;YE Yong-sheng(Huaibei Normal University, Huaibei 235000, China)

机构地区：[1]淮北师范大学,安徽淮北235000

出　　处：《廊坊师范学院学报（自然科学版）》2018年第1期119-120,128,共3页Journal of Langfang Normal University(Natural Science Edition)

基　　金：安徽省教育厅教育教学研究项目(2016jyxm0932);安徽省大规模在线开放课程(MOOC)示范项目(2015mooc053);安徽省大学数学系列课程教学团队(2015jxtd120);淮北师范大学教学研究重点项目(jy2017105)

摘　　要：利用变量变换法,研究了二阶变系数齐次线性微分方程的通解求法,给出了二阶变系数齐次线性微分方程转化为欧拉方程的充要条件,同时,得出特殊情形时的结果。By using the variable transformation method,this paper studies the general solution of second order homogeneous linear differential equations with variable coefficients.A sufficient and necessary condition for the second order homogeneous linear differential equations with variable coefficients transformed into Euler equation is derived out.Moreover,some results of the special conditions for the linear equations are obtained.

关 键 词：变系数 线性 微分方程 变量变换 

分 类 号：O175.1[理学—数学]