Geodesic
On one linear equation of the Euler type
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 74-83.

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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. 
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R. Mustafokulov. On one linear equation of the Euler type. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 74-83. http://geodesic.mathdoc.fr/item/INTO_2021_192_a7/

[1] Gursa E., Kurs matematicheskogo analiza, v. 2, Nauka, M., 1936

[2] Erugin N. P., “Privodimye sistemy”, Tr. Mat. in-ta im. V. A. Steklova., 13 (1946), 3–96

[3] Matveev N. M., Obyknovennye differentsialnye uravneniya, SPb., 1996

[4] Mustafokulov R., “Modelnoe uravnenie dlya odnogo lineinogo odnorodnogo uravneniya tipa Eilera $n$-go poryadka”, Dokl. AN Resp. Tadzhikistan., 61:3 (2018), 216–223

[5] Mustafokulov R., “Integralnoe predstavlenie resheniya odnogo lineinogo uravneniya tipa Eilera v sluchae prostykh kharakteristik”, Sovremennye metody teorii kraevykh zadach, Mat. Mezhdunar. konf. «Voronezhskaya vesennyaya matematicheskaya shkola «Pontryaginskie chteniya–XXX» (3–9 maya 2019 g., Voronezh), Voronezh, 2019, 211–212

[6] Mustafokulov R., “Ob odnom lineinom uravnenii tipa Eilera s kratnoi kharakteristikoi”, Tr. Mezhdunar. nauch. konf., posv. 100-letiyu prof. S. G. Kreina, Voronezh, 2017, 140–143

[7] Stepanov V. V., Kurs differentsialnykh uravnenii, Fizmatgiz, M., 1959

[8] di Bruno F., “Note sur une nouvelle formule de calcul différentiel”, Quart. J. Pure Appl. Math., 1 (1857), 359–360

[9] Radjabov N., “Integral representation of the manifold solution for new class of the Volterra-type integral equations with boundary singularity in case when kernel contian logaritmic singularity and its power”, J. Math. System Sci., 6 (2016), 23–37

[10] Radjabov N., “Volterra-type integral equations with super singular kernel”, Functional Analysis in Interdisciplinary Applications, Springer-Verlag, 2017, 312–319