| 具有特殊解结构的二阶线性微分方程的可积性判据 |
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| 引用本文： | 解加芳,翟磊军,邹杰涛.具有特殊解结构的二阶线性微分方程的可积性判据[J].数学的实践与认识,2011,41(14). |
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| 作者姓名： | 解加芳 翟磊军 邹杰涛 |
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| 作者单位： | 北方工业大学理学院,北京,100144 |
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| 摘 要： | 针对二阶线性微分方程y″+p(x)y′+q(x)y=0具有某种特殊解结构的情况下,进行可积性判据研究,利用降阶的思想,得到p(x),q(x)满足的关系式,找到了方程可积的充分条件.
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| 关 键 词： | 二阶线性微分方程 降阶 充分条件 可积判据 通解 |
Integral Criterion of Second Order Linear Differential Equation Possessing Particular Solution |
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| XIE Jia-fang,Zhai Lei-jun,ZOU Jie-tao.Integral Criterion of Second Order Linear Differential Equation Possessing Particular Solution[J].Mathematics in Practice and Theory,2011,41(14). |
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| Authors: | XIE Jia-fang Zhai Lei-jun ZOU Jie-tao |
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| Abstract: | In this paper,the integral criterions of the second order linear differential equation(1), which has a kind of particular solution,are investigated.The relations both p(x)and q(x)are derived by the method of reduction order,and the integrable sufficient conditions of differential equation are found. |
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| Keywords: | second order linear differential equation the method of reduction order sufficient condition integral criterion general solution |
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