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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 893–901 (Mi semr1101)

Differentical equations, dynamical systems and optimal control

On some properties of first order algebraic differential equations

A. Y. Yanchenko, V. A. Podkopaeva

National Research University «MPEI», 14, Krasnokazarmennaya str., Moskow, 111250, Russia

Abstract: The paper deals with first-order algebraic differential equations. Installed effective necessary conditions under which such equations have one of the solutions of an entire function finite order. It is also proved that in this case every solution of such an equation is a solution of some linear homogeneous differential equation of a special type.

Keywords: algebraic differential equation, entire function, linear homogeneous differential equation.

DOI: https://doi.org/10.33048/semi.2019.16.059

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UDC: 517.925
MSC: 34A09
Received February 15, 2019, published June 25, 2019

Citation: A. Y. Yanchenko, V. A. Podkopaeva, “On some properties of first order algebraic differential equations”, Sib. Èlektron. Mat. Izv., 16 (2019), 893–901

Citation in format AMSBIB
\Bibitem{YanPod19} \by A.~Y.~Yanchenko, V.~A.~Podkopaeva \paper On some properties of first order algebraic differential equations \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 893--901 \mathnet{http://mi.mathnet.ru/semr1101} \crossref{https://doi.org/10.33048/semi.2019.16.059} `