微分方程解的定性研究。（反对称微分形式的应用）
Qualitative investigation of the solutions to differential equations. (Application of the skew-symmetric differential forms)
摘要：
所提出的研究微分方程解的方法并不新鲜。这种方法是由嘉当在他的分析可积性的微分方程。在这里，这种方法概述了反对称微分形式的作用。反对称微分形式在微分方程解的定性研究中的作用取决于这样一个事实，即这些形式的数学工具使人们能够确定微分方程或微分方程组的各种元素的一致性条件。例如，这使得人们能够定义偏微分方程中偏导数的一致性，微分方程组中微分方程的一致性，常微分方程中函数导数和初值导数的共轭性等，微分方程解的函数性质只取决于是否满足共轭条件都很满意
英文摘要：
The presented method of investigating the solutions to differential equations is not new. Such an approach was developed by Cartan in his analysis of the integrability of differential equations. Here this approach is outlined to demonstrate the role of skew-symmetric differential forms. The role of skew-symmetric differential forms in a qualitative investigation of the solutions to differential equations is conditioned by the fact that the mathematical apparatus of these forms enables one to determine the conditions of consistency for various elements of differential equations or for the system of differential equations. This enables one, for example, to define the consistency of the partial derivatives in the partial differential equations, the consistency of the differential equations in the system of differential equations, the conjugacy of the function derivatives and of the initial data derivatives in ordinary differential equations and so on. The functional properties of the solutions to differential equations are just depend on whether or not the conjugacy conditions are satisfied.
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