| 饶梦真1，谭钦洋1，齐静2，张昕1.浅述积分因子与方程解的联系[J].海南师范大学学报自科版,2020,33(3):280-286 |
| 浅述积分因子与方程解的联系 |
| Relation Between Integral Factor and Equation Solution |
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| DOI：10.12051/j.issn.1674-4942.2020.03.007 |
| 中文关键词: 微分方程 积分因子 雅可比行列式 函数相关 性质 |
| 英文关键词: differential equation integral factor Jacobian determinant function correlation property |
| 基金项目: |
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| 摘要点击次数: 920 |
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| 中文摘要: |
| 文章简述了几类微分方程及其积分因子的形式，给出积分因子的相关性质，叙述了如
何利用一个方程的两个不同的积分因子对方程进行快速求解，在此过程中引用了雅可比行列式为
零的相关结论（函数相关的结论），修正了文献中的一处不足，证明了一个方程中两个积分因子之
间的函数关系，最后给出了一类齐次微分方程的快速求解法。 |
| 英文摘要: |
| In this paper, several kinds of differential equations and the forms of their integral factors were briefly intro⁃
duced, the related properties of the integral factors were mainly given, and how to use two different integral factors of an
equation to solve the equation quickly was described. In this process, the related conclusion that Jacobian determinant is ze⁃
ro (function related conclusion) was quoted, and one of the shortcomings in reference was corrected. The functional relation⁃
ship between two integral factors in an equation was proved. Finally, a fast solution of a class of homogeneous differential
equation was given. |
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