二阶变系数线性微分方程求解问题的新探索  

Some New Conclusions Based on the Solution of the Second Order Linear Differential Equation

作　　者：邓治 DENG Zhi(Department of Mathematics, Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学系,广州510006

出　　处：《大学数学》2017年第6期122-126,共5页College Mathematics

基　　金：广东省自然科学基金(2016A030310258)

摘　　要：二阶常系数线性微分方程的求解理论,目前已经比较完善.然而对于二阶变系数线性微分方程,其求解问题的研究仍处于发展状态中.本文在文献[3-5]的基础上,利用降阶法、线性变换法及Raccati方程的等价性得到若干个可写出通解的二阶变系数线性微分方程的新类型,尤其关于可转化为f″+gf=0二阶线性微分方程有了一些结果.The solving theory of the second order constant coefficient linear differential equation,.But for the second order linear differential equation with variable coefficients,the research is still in the state of development to solve the problem.In this paper,based on the literature[3-5],we obtain some new types of linear differential equations with variable coefficients by using the reduced order method,the linear transformation method and the Equivalence of the Raccati equation,which can be used to write out the general solution of the two order variable coefficients.In particular,there are some results for two order linear differential equations which can be transformed intof″+gf=0.

关 键 词：二阶变系数线性微分方程 降阶法 线性变换法 

分 类 号：O175.1[理学—数学]