| 方程f（x,y）dx＋g（x,y）dy=0的首次积分的存在性 |
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| 引用本文： | 黄吉祥.方程f（x,y）dx＋g（x,y）dy=0的首次积分的存在性[J].华东师范大学学报(自然科学版),1996(4):33-37. |
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| 作者姓名： | 黄吉祥 |
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| 作者单位： | 华东师范大学数学系 |
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| 摘 要： | 本文通过连续可微的局部积分因子并应用有限覆盖定理。证明了方程ｆ（ｘ，ｙ）ｄｘ＋ｇ（ｘ，ｙ）ｄｙ＝０在其无奇点的单边通有界闭域的内部，存在连续可微的积分因子及其相应的首次积分。
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| 关 键 词： | 奇点 积分因子 首次积分 单连通区域 存在性 |
Existence of the First Integral for the Equation f(x,y)dx+g(x,y)dy=0 |
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| Huang Jixiang.Existence of the First Integral for the Equation f(x,y)dx+g(x,y)dy=0[J].Journal of East China Normal University(Natural Science),1996(4):33-37. |
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| Authors: | Huang Jixiang |
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| Institution: | East China Normal University. Shanghai 200062 |
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| Abstract: | By constructing continuously differentiable local integrating factors and using the finite covering theorem, it is proved in this paper for the equation f(x,y)dx+g(x,y)dy= 0 that, in the interior of any simply connected and bounded closed region without singular points, there existcontinuously defferentiable integrating factors and corresponding first integrals. |
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| Keywords: | singular point integrating factor first integral simply connected region |
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