The solution of a class of linear differential equations via functions of the Mittag-Leffler type

Abstract

Numerous individual classes of ordinary differential equations are known to be integrable in quadratures (e.g., see [1, p. 18; 2, p. 290 of the Russian translation; 3, p. 13]). Various methods are used for finding explicit solutions of such equations, and the solutions themselves are often expressed via special functions. Naturally, the appearance of new classes of special functions results in new classes of differential equations integrable in quadratures.