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| 一类可积的三阶线性微分方程 | |
| 引用本文： | 张有珍,闫运生. 一类可积的三阶线性微分方程[J]. 河南教育学院学报(自然科学版), 2009, 18(1): 15-16 |
| 作者姓名： | 张有珍 闫运生 |
| 作者单位： | 1. 郑州轻工职业学院基础部,河南郑州,450002 2. 河南工业大学理学院,河南郑州,450052 |
| 摘 要： | 借助自变量代换,获得了三阶变系数线性微分方程的新的可积类型,并且得到了方程y^″′＋p（x）y^″＋q（x）y′＋r（x）y=0 化为常系数线性微分方程的充要条件． |
| 关 键 词： | 线性微分方程 通解 充要条件 |
An Intergrable Form of Third Order Linear Differential Equation |
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| ZHANG Youzhen,YAN Yunsheng. An Intergrable Form of Third Order Linear Differential Equation[J]. Journal of Henan Education Institute(Natural Science Edition), 2009, 18(1): 15-16 | |
| Authors: | ZHANG Youzhen YAN Yunsheng |
| Affiliation: | a.Department of Basics;Zhengzhou Vocational Colloge of Light Industry;Zhengzhou 450002;China;b.College of Science;Henan University of Technology;Zhengzhou 450052;China |
| Abstract: | By means of variable substitute,a new integrable form of third order linear differential equation was obtained. Particularly, a necessary and sufficient condition of equation eqution y^″′＋p（x）y^″＋q（x）y′＋r（x）y=0 converting to third order linear differential eqution with constants coefficients form was proved. |
| Keywords: | linear differential equation general solution necessary and sufficient condition |
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