非恰当微分方程三类对称式积分因子
Three Symmetric Form Integrating Factors of Non-Exact Differential Equations
DOI: 10.12677/aam.2024.138360, PDF,    国家自然科学基金支持
作者: 张子诺：桂林理工大学数学与统计学院，广西 桂林；蒋宜蓉：广西民族大学数学与物理学院，广西 南宁；谢 海*：桂林理工大学数学与统计学院，广西 桂林；广西高校应用统计重点实验室，广西 桂林；桂林理工大学大数据处理与算法技术研究中心，广西 桂林
关键词: 非恰当微分方程；恰当微分方程；积分因子；Non-Exact Differential Equations； Exact Differential Equations； Integrating Factors
摘要: 利用积分因子把非恰当微分方程转化为恰当微分方程是求解非恰当微分方程的重要手段。如何寻找合适的积分因子是转化问题关键之所在。首先，给出非恰当微分方程存在三种类型积分因子的充要条件。然后，给出相应的例子说明这些充要条件的应用。最后，对这些充要条件进行简单总结并提出一些研究展望。
Abstract: It is an important means to solve non-exact differential equations by transforming them to exact differential equations using integral factors. How to find the appropriate integrating factors is the key to the transformation problem. Firstly, we present the sufficient and necessary conditions for the existence of three types of integral factors for non-exact differential equations. Then, some examples are given to illustrate the application of these necessary and sufficient conditions. Finally, these necessary and sufficient conditions are summarized briefly and some research prospects are put forward.
文章引用：张子诺, 蒋宜蓉, 谢海. 非恰当微分方程三类对称式积分因子[J]. 应用数学进展, 2024, 13(8): 3778-3787. https://doi.org/10.12677/aam.2024.138360

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