Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-12T23:33:19.014Z Has data issue: false hasContentIssue false
  • English
  • Français

An autonomous system of differential equations in the plane

Published online by Cambridge University Press:  17 April 2009

R.F. Matlak
R.F. Matlak
Affiliation:
Macquarie University, North Ryde, New South Wales.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the present note the equation yn = x1-m ym is reduced, under appropriate conditions, to a quadratic autonomous system of differential equations in the plane. In pursuance of this new approach, the main geometric features of this autonomous system are determined and a method of solving it is outlined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 391 - 395
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Abel, Niels Henrik, Sur l'équation differentielle (y+s)dy + (p+qy+ry2)dx = 0 (Oeuvres, Vol. 2; Christiania, 1881 Reprinted Johnson, New York, 1965).Google Scholar
[2]Bautin, N.N., “On periodic solutions of a system of differential equations” (Russian), Akad. Nauk. SSSR. Prikl. Mat. Meh. 18 (1954), 128.Google Scholar
[3]Bellman, R., Stability theory of differential equations (McGraw-Hill, New York, 1953).Google Scholar
[4]Chandrasekhar, S., An introduction to the study of stellar structure (Chicago University Press, 1939. Reprinted Dover, New York, 1957).Google Scholar
[5]Coppel, W.A., “A survey of quadratic systems”, J. Differential Equations 2 (1966), 293–304.Google Scholar
[6]Davis, Harold T., Introduction to nonlinear differential and integral equations (Dover, New York, 1962).Google Scholar
[7]Hille, E., “On the Thomas-Fermi equation”, Proc. Nat. Acad. Sci. USA 62 (1969), 7–10.Google Scholar
[8]Hille, E., “Some aspects of the Thomas-Fermi equation”, J. Analyse Math. (to appear).Google Scholar
[9]Hille, E., “Aspects of Emden's equation”, (to appear).Google Scholar
[10]Kamke, E., Differentialgleichungen: Lösungsmethoden und Lösungen, I (Gewöhnliche Differentialgleichungen), 7th ed. (Akad. Verlagsgesellschaft, Leipzig, 1961).Google Scholar
[11]Lefschetz, Solomon, Differential equations: Geometric theory, 2nd ed. (Interscience, New York, 1963).Google Scholar
[12]Poincaré, H., Mémoire sur les courbes définies par une équation différentielle (Oeuvres, Vol. 1; Gauthier-Villars, Paris, 1928).Google Scholar