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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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

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On the Solution of a Two-parameter Second-order Equation with a Polynomial Right-hand Side

Author(s):

Zilya Nailevna Khakimova

Mozhaisky Military Space Academy

vka@mil.ru

Abstract:

A two-parameter class of ordinary differential equations of the 2nd order with a polynomial right-hand side is considered. A two-parameter power-law transformation is found that transforms the original class of equations with arbitrary essential exponents into an equation with fixed exponents with variables. General solutions of all equations of the studied class of equations are found. We also found general solutions for 11 more two-parameter classes of polynomial and fractional-polynomial equations, which are related to the original class of equations by transformations that are generators of the 12th order dihedral group.

Keywords

References:

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