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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021 Volume 192, Pages 74–83 (Mi into783)

This article is cited in 1 paper

On one linear equation of the Euler type

R. Mustafokulov

Tajik National University, Dushanbe

Abstract: In this paper, for an Euler-type linear equation of order $n$, we indicate a change of variable and conditions for the coefficients under which the equation is reduced to an equation with constant coefficients. For a solution of the inhomogeneous equation, we construct an explicit integral representation depending on the roots of the characteristic equation.

Keywords: linear equation of Euler type, model equation, characteristic of equation, fundamental solution, determinant of Vandermonde type.

UDC: 517.55

MSC: 34B45, 35L05

DOI: 10.36535/0233-6723-2021-192-74-83



© Steklov Math. Inst. of RAS, 2025