AAM  >> Vol. 5 No. 1 (February 2016)

    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

  • 全文下载: PDF(379KB) HTML   XML   PP.87-97   DOI: 10.12677/AAM.2016.51013  
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作者:  

陈雄:海南师范大学数学与统计学院,海南 海口;仪陇县第二中学,四川 南充;
林诗游,张皓涵:海南师范大学数学与统计学院,海南 海口

关键词:
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

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.

文章引用:
陈雄, 林诗游, 张皓涵. 二阶变系数线性微分方程化为标准型的求解[J]. 应用数学进展, 2016, 5(1): 87-97. http://dx.doi.org/10.12677/AAM.2016.51013