| n阶常系数非齐次线性微分方程的通解 |
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| 引用本文： | 唐生强,唐清干.n阶常系数非齐次线性微分方程的通解[J].湖南农业大学学报(自然科学版),2004,30(5):478-481. |
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| 作者姓名： | 唐生强 唐清干 |
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| 作者单位： | 桂林电子工业学院图书馆,广西,桂林,541004;桂林电子工业学院计算科学与数学系,广西,桂林,541004 |
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| 基金项目： | 广西区教育厅资助项目(D20010) |
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| 摘 要： | 为研究n阶常系数非齐次线性常微分方程解的问题，求证了n阶常系数非齐次线性常微分方程的通解和特解的积分表达式．利用韦达定理和一个变量替换，对n阶常系数非齐次线性微分方程进行降阶，导出该方程的一个用积分表示的通解公式，并根据特征根的不同情形给出了通解的各种形式及相应的通解和特解公式．
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| 关 键 词： | 阶常系数非齐次线性微分方程 通解 特解 韦达定理 |
| 文章编号： | 1007-1032(2004)05-0478-04 |
| 修稿时间： | 2004年3月18日 |
The General Solution Derivation of Order n Non-homogeneous Linear Differential Equation with Constant Coefficients |
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| TANG Sheng-qiang,TANG Qing-gan.The General Solution Derivation of Order n Non-homogeneous Linear Differential Equation with Constant Coefficients[J].Journal of Hunan Agricultural University,2004,30(5):478-481. |
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| Authors: | TANG Sheng-qiang TANG Qing-gan |
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| Institution: | TANG Sheng-qiang1,TANG Qing-gan2 |
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| Abstract: | To obtain the general solution and their special solutions in integration form,the way to get the n order non-homogeneous linear ordinary equation with constant coefficients was studied.Resorting to the theory of Vieta and an alternative transformation,the order of the equation is lowered and a general solution formula,expressed by integrations was derived.According to root cases of the auxiliary equation,the detailed expressions of the general solution and their special solutions were given. |
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| Keywords: | order n non-homogeneous linear differential equation with constant coefficients general solution special solutions the theory of Vieta |
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