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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 139–146 (Mi ufa175)  

Two-dimensional algebras of dynamic symmetries of ODEs

M. I. Timoshin

Ulyanovsk State Technical University, Ulyanovsk, Russia

Abstract: The efficiency of use of dynamical symmetries at research of integrability of differential equations is shown in this work. The generalization of S. Lie's classification of ordinary differential equations of the second order with respect to twodimensional algebras of point symmetries is constructed. Integrable cases of second order special type ODE are indicated. It is noted that a part of the found integrability cases is related to Abel's type equations and apparently represents independent interest.

Keywords: dynamic symmetries, invariants, two-dimensional algebras, Riccati equation, Abel equation.

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UDC: 517.9
Received: 02.08.2011

Citation: M. I. Timoshin, “Two-dimensional algebras of dynamic symmetries of ODEs”, Ufimsk. Mat. Zh., 4:4 (2012), 139–146

Citation in format AMSBIB
\Bibitem{Tim12}
\by M.~I.~Timoshin
\paper Two-dimensional algebras of dynamic symmetries of ODEs
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 4
\pages 139--146
\mathnet{http://mi.mathnet.ru/ufa175}


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  • http://mi.mathnet.ru/eng/ufa/v4/i4/p139

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