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方辉平, 叶鸣. 二阶变系数齐线性常微分方程的求解[J]. 重庆工商大学学报(自然科学版), 2011, 28(1): 14-17.

被以下文章引用:

• 标题: 二阶变系数线性微分方程化为标准型的求解Solution of Two Order Variable Coefficient Linear Differential Equation into Standard Form

  作者: 陈雄, 林诗游, 张皓涵

  关键字: 二阶变系数, 线性微分方程, 标准型, 余函数, 特积分, 通解Two Order Variable Coefficient, Linear Differential Equation, Standard Type, Cofunction, Particular Integral, General Solution

  期刊名称: 《Advances in Applied Mathematics》, Vol.5 No.1, 2016-02-26

  摘要: 本文给出关于二阶变系数线性微分方程的求解，转变以往降阶的常规思维，利用其标准型进行求解。在标准型的求解中，通过对原微分方程的化简，利用余函数和特积分，分别求出其标准型齐次和非齐次的解，最后构造出原方程通解。 This paper discusses the solution of the two order variable coefficient linear differential equation with standard type, which transforms the traditional method of reducing order. Through simpli-fying the original differential equation and using means of cofunction and particular integral, we can get the homogeneous and non-homogeneous solution of the standard type. Finally we can construct the general solution of the original equation.