| 一类二阶变系数非齐次线性微分方程的通解 |
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| 引用本文： | 李永利,何晓娜.一类二阶变系数非齐次线性微分方程的通解[J].高师理科学刊,2011,31(3):45-47. |
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| 作者姓名： | 李永利 何晓娜 |
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| 作者单位： | 河南质量工程职业学院,5年制专科部,河南,平顶山,467000 |
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| 摘 要： | 受一类二阶常系数非齐次线性微分方程y″+py′+qy=f(x)(其中:p=λ1+λ2;q=λ1λ2)通解的简便求法启发,给出了求一类二阶变系数非齐次线性微分方程y″+p(x)y′+q(x)y=f(x)(其中:p(x)=λ1(x)+λ2(x);q(x)=λ1'(x)+λ1(x)λ2(x))的通解的方法.
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| 关 键 词： | 二阶变系数非齐次线性微分方程 降阶法 通解 |
The general solution for a kind of two-order variable coefficient inhomogeneous linear differential equation |
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| LI Yong-li,HE Xiao-na.The general solution for a kind of two-order variable coefficient inhomogeneous linear differential equation[J].Journal of Science of Teachers＇College and University,2011,31(3):45-47. |
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| Authors: | LI Yong-li HE Xiao-na |
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| Institution: | LI Yong-li,HE Xiao-na(Department of Five-years College,Henan Quality Polytechnic,Pingdingshan 467000,China) |
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| Abstract: | By using the simple method of general solution for a kind of two-order constant coefficient inhomogeneous linear differential equation y″＋py′＋qy =f（x）（p=λ1 ＋ λ2,q=λ1 λ2）,obtained general solution for a kind of two-order variable coefficient inhomogeneous linear differential equation y″＋p（x）y′＋q（x）y =f（x）（p（x）= λ1（x） ＋ λ2（x）,q（x）=λ1′（x） ＋λ1（x） λ2（x））. |
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| Keywords: | two-order variable coefficient inhomogeneous linear differential equation method of reduction of order general solution |
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