Файл	Ном	Сабт карда шуд
Ergashboeva Tursunboy	STUDY OF LINEARIZABILITY CHARACTERS OF THE RIKKATI EQUATION WITH THE TWO – DIMENSIONAL LIE ALGEBRA	9

Authors: Ergashboeva Tursunboy – Dotsent of the Department of Mathematical Analysis named after Professor A.Mukhsinov State Educational Instituon “KhSU named after academician B. Gafurov” (Tajikistan Republic, Khujand), Vositova Dilorom Abdurasulovna – Dotsent of the Department of Mathematical Analysis named after Professor A.Mukhsinov, State Educational Instituon “KhSU named after academician B. Gafurov” (Tajikistan Republic, Khujand)

JOURNAL NUMBER: 3(62). YEAR OF ISSUE: 2022. LANGUAGE OF THE ARTICLE: Russian

ANNOTATION

The Riccati equation is a non-linear differential equation. Joseph Liouville showed in 1841 that the solution of the special Riccati equation in the general case cannot be represented as an integration of elementary functions. In this paper, the Riccati equation is considered from the point of view of group analysis of differential equations. A theorem on the solvability of the Riccati equation is proved, which admits a two-dimensional Lie algebra. The proof of the theorem contains a construction for constructing solutions to the Riccati equation and, therefore, has theoretical and practical significance

KEY WORDS

Riccati equations, Lie group, Lie algebra, operator, group operator, commutator.  

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