Integrals of Lappo-Danilevsky Multidimensional Differential System
Author(s):
Viktor Gorbuzov
Department of mathematical analysis,
differential equations and algebra,
Faculty of Mathematics and Information Science,
Yanka Kupala State University of Grodno,
Ozeshko str. 22, Grodno,
Republic of Belarus, 230023
gorbuzov@grsu.by
Andrei Pranevich
Department of mathematic and software support for economic systems,
Faculty of Economics and Management,
Yanka Kupala State University of Grodno,
Ozeshko str. 22, Grodno, Republic of Belarus, 230023
pranevich@grsu.by
Abstract:
In this article we consider a completely solvable real non-autonomous linear system
of Lappo-Danilevsky exact differential equations. For this system the spectral method of
the integral basis construction has been elaborated. Using common
eigenvectors and generalized eigenvectors of the integral matrices of a completely
solvable Lappo-Danilevsky system we get real first integrals of this system in explicit form.
The explicit forms of first integral, which depend on the multiplicity of
integral matrices primer divisors, are given, and
the sufficient conditions of the existence of autonomous first integrals
for this differential system has been obtained. In addition, some examples
are given to illustrate the results.
Keywords: system of total differential equations, first integral.
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