| 一类一阶二次微分方程解的探究 |
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| 引用本文： | 龚东山,牛富俊,刘岳巍.一类一阶二次微分方程解的探究[J].西安文理学院学报,2008,11(4):28-31. |
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| 作者姓名： | 龚东山 牛富俊 刘岳巍 |
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| 作者单位： | [1]兰州大学数学与统计学院,甘肃兰州730000 [2]中国科学院寒区旱区环境与工程研究所冻土工程国家重点实验室,甘肃兰州730000 |
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| 基金项目： | 国家自然科学基金，中国科学院"西部之光"人才培养计划 |
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| 摘 要： | 为了探究一类一阶二次微分方程的解析解，先提出独立通解（UGS）的概念，可以得到齐次微分方程的解，其通解是由若干个独立通解共同构成的．对于非齐次情形，其解是由若干个特解共同构成，并验证了这些特解线性相关．
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| 关 键 词： | 一阶二次 微分方程 线性无关 独立通解 特解 线性相关 |
Research of Solutions of a Kind of First-order and Two-degree Differential Equations |
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| GONG Dong-shan,NIU Fu-jun,LIU Yue-wei.Research of Solutions of a Kind of First-order and Two-degree Differential Equations[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2008,11(4):28-31. |
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| Authors: | GONG Dong-shan NIU Fu-jun LIU Yue-wei |
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| Institution: | GONG Dong-shan ,NIU Fu-jun ,LIU Yue-wei ( 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China; 2. State Key Laboratory of Frozen Soil of Engineering , Cold and Arid Regions Environmental and Engineering Research Institute , Chinese Academy of Sciences, Lanzhou 730000, China ) |
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| Abstract: | In the process of finding analytic solutions of a kind of first-order and two - degree differential equations, the conception of undependent general solution is firstly presented. Based on this conception, we get the solutions of homogeneous differential equation which are constructed by some undependent general solutions. For the non-homogeneous differential equation, we prove the solutions are constructed by some special solutions which are linear independence. |
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| Keywords: | first - order and two-degree differential equation linear independence undependent general solution special solution linear dependence |
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