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ON THE INTEGRATION OF ONE FOUR-PARAMETER CLASS OF FRACTIONAL-POLYNOMIAL ORDINARY DIFFERENTIAL EQUATIONS

Khakimova Zilya Nailyevna  (PhD in Physics and Mathematics Mozhaisky Military Space Academy )

This article discusses various classes of ordinary differential equations of the 2nd order - power, polynomial and fractional-polynomial types. Using the method of discrete invariants and their generalizations, several three-parameter classes of ordinary differential equations with power and polynomial right-hand sides, as well as (for the first time) a four-parameter class of equations with fractional-polynomial right-hand sides, were integrated. A way is indicated for «multiplying» the found solvable subclasses of equations by a discrete group of transformations in the class of fractional-polynomial ordinary differential equations and obtaining new solvable subclasses of equations.

Keywords:ordinary differential equation, exact solution of an ordinary differential equation, discrete transformation group, dihedral group, invariant of a discrete transformation, concomitant, classes of power, polynomial and fractional-polynomial differential equations
 

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Citation link:
Khakimova Z. N. ON THE INTEGRATION OF ONE FOUR-PARAMETER CLASS OF FRACTIONAL-POLYNOMIAL ORDINARY DIFFERENTIAL EQUATIONS // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2026. -№01. -С. 163-166 DOI 10.37882/2223-2966.2026.01.34
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