一类一阶二次微分方程解的探究  

Research of Solutions of a Kind of First-order and Two-degree Differential Equations

作　　者：龚东山[1] 牛富俊[2] 刘岳巍[1] 

机构地区：[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

出　　处：《西安文理学院学报（自然科学版）》2008年第4期28-31,共4页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金对外交流与合作项目(40640420072);中科院西部之光联合学者项目

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.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.

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 

分 类 号：O175.1[理学—数学]