ON THE INTEGRABILITY OF A CLASS OF DIFFERENTIAL EQUATIONS - Zlatanovska, Biljana; Piperevski, Boro M. (Matematichki Bilten, 2021)
In this paper, a class of second-order linear differential equations is reviewed. For this class of B.S.Popov necessary and suffcient condition for reductable according to Frobenius is obtained. By using another method, the same condition is obtained where the existence of the natural number \(n\) is replaced by the existence of an integer \(n\). For the same class of second-order linear differential equations, the case for reductable according to Frobenius which is independent from an exist of a number \(n\) is reviewed. In both cases, formulas of one particular solution and transformation to a system of first-order differential equations are obtained. In end, this theory is supported by examples.