| 关于d(y/x)=((λx~n+sum1tona_iy~ix~(n_(-i)))/(-y~n+sum0ton-1b_iy~ix~(n_(-i))))的积分曲线 |
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| 引用本文： | 李梧生.关于d(y/x)=((λx~n+sum1tona_iy~ix~(n_(-i)))/(-y~n+sum0ton-1b_iy~ix~(n_(-i))))的积分曲线[J].汕头大学学报(自然科学版),1986(1). |
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| 作者姓名： | 李梧生 |
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| 作者单位： | 汕头大学数学系 |
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| 摘 要： | 记所论微分方程为(E_λ)_n,本文给出(E_λ)_n 基本型阵、实际型阵的定义和求法,用实际型阵表达λ遍取不同实数值时,(E_λ)_n积分曲线的定性变化图景.对(E_λ)_1、(E_λ)_2求得全部基本型阵和实际型阵,对(E_λ)_3、(E_λ)_4求得全部基本型阵,阐明可实现性,给出求实际型阵的典型例子.本文原则上适用于 n≥5的情形.
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| 关 键 词： | 积分曲线 微分方程定性论 |
Integral Curves of the Differential Equation |
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| Li Wusheng.Integral Curves of the Differential Equation[J].Journal of Shantou University(Natural Science Edition),1986(1). |
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| Authors: | Li Wusheng |
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| Institution: | Department of Mathematics |
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| Abstract: | The differential equation in the heading is denoted by (E_λ)_n. (λ varies from -∞ to +∞).In this paper,a corresponding relation between the qualitative picture and the“type-matrix”of the (E_λ)_n is established. The“basal type-matrix” of the (E_λ)_n(n=1,2,3,4) and the “actual type- matrix”of the (E_λ)_n(n=1,2) are found. The general method to find the“actual type-matrix” is showed.A typical example is given. |
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| Keywords: | Integral curves Qualitative theory of ordinary differential equations |
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