Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the 3rd Order ODEs Having Lie-symmetries and First Integrals

Author(s):

P. P. Avrashkov

Oryol State Technical University,
Naugorskoe shosse 29, Oryol

avrashkov@mail.ru

V. F. Zaitsev

Russian State Pedagogical University,
nab. r. Moyki 48, Saint-Petersburg

valentin_zaitsev@mail.ru

Abstract:

We consider the 3-rd order ordinary differential equations:
y'''=F(x,y).
We proved that the class of ODEs has only 25 special subclasses of the nonlinear equations. These equations admit a Lie point symmetry and have quadratic (on y'') first integrals.

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