Singular points classification of first order differential equations system not solved for derivatives

  • Khusanov Bazar Associate Professor of the “Higher mathematics” department of the Samarkand architecture and civil engineering institute, Samarkand, Uzbekistan
  • Kulmirzaeva Gulrabo Abduganievna senior techer of the “Higher mathematics” department of the Samarkand architecture and civil engineering institute, Samarkand, Uzbekistan
DOI: https://doi.org/10.17605/ijie.v4i3.1533
Keywords: singular point, classification, image, integral linear surface, equivalent, family, types, focus, non-descending, parabolic, oscillate

Abstract

 The article considers the singular system points’ classification of first-order differential equations that are not resolved with respect to derivatives. By displaying using some ratios that considered integral curves locations by special point in space taking into account the mutually located integral parabolas we obtain the corresponding pictures of the integral curves location by the singular system point. The types of singular equation points can be classified according the characteristic equation roots type, which we call a saddle, node, focus, center, or saddle focus

References

L.V.Pkhakadze and A.A. Shestakov Mathematical collection, 49 (91). №1-2, 1959

T. Hayasi Nonlinear Oscillations in Physical Systems. Publishing house "Mir", М. 1968

Sh.R.Sharipov, N.S.Muminov. Simple differential equations «Teacher», Tashkent, 1992

B. Khusanov, Sh.R.Sharipov, S.Kh. Mamashev. On some questions of trajectories in n-dimensional generalized-homogeneous system. – Izvestia of the Academy of Sciences of the Kaz SSR. Series of Physics - Mathematical Sciences, 1981, №3, P.38-43

Published
2021-04-02
How to Cite
[1]
Khusanov Bazar and Kulmirzaeva Gulrabo Abduganievna 2021. Singular points classification of first order differential equations system not solved for derivatives. International Journal on Integrated Education. 4, 3 (Apr. 2021), 448-450. DOI:https://doi.org/10.17605/ijie.v4i3.1533.
Issue
Vol. 4 No. 3 (2021): IJIE
Section
Articles

Copyright (c) 2021 Khusanov Bazar, Kulmirzaeva Gulrabo Abduganievna

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