| 一种二阶变系数线性微分方程的求解方法 |
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| 引用本文： | 胡劲松 李先富 郑克龙. 一种二阶变系数线性微分方程的求解方法[J]. 重庆工商大学学报(自然科学版), 2005, 22(3): 220-222 |
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| 作者姓名： | 胡劲松 李先富 郑克龙 |
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| 作者单位： | 1. 西华大学,数学系,四川,成都,610039
2. 西南科技大学,理学院,四川,绵阳,621002 |
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| 摘 要： | 在知道二阶变系数线性齐次微分方程一个特解的情况下,通过常数变易法,将二阶变系数线性非齐次微分方程转化为一阶线性微分方程,从而给出运算量较小的二阶变系数线性非齐次微分方程通解的一般公式,也给出了用刘维尔定理求解二阶变系数线性齐次微分方程的一个理论依据.
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| 关 键 词： | 二阶变系数线性微分方程 常数变易法 通解 |
| 文章编号： | 1672-058X(2005)03-0220-03 |
One method for solving the various coefficient linear differential equation |
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| HU Jin-song~,LI Xian-fu~,ZENG Ke-long~. One method for solving the various coefficient linear differential equation[J]. Journal of Chongqing Technology and Business University:Natural Science Edition, 2005, 22(3): 220-222 |
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| Authors: | HU Jin-song~ LI Xian-fu~ ZENG Ke-long~ |
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| Affiliation: | HU Jin-song~1,LI Xian-fu~2,ZENG Ke-long~2 |
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| Abstract: | On the basis of knowing a special solution of the various coefficient linear differential equation of order 2 and by using the method of variation of constant, the various coefficient linear differential equation of order 2 is transferred to the linear differential equation of 1-order, and a general formula of general solution of the various coefficient non-homogeneous linear differential equation of order 2 is derived. It also gives a theoretical foundation of solving the various coefficient homogeneous linear differential equation of order 2 according to Liouville theorem. |
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| Keywords: | various coefficient linear differential equation variation of constants method general solution |
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