We present a classification of irregular singular points and infinity of second-order linear differential equations; Furthermore, we show some Wronskian results of the solutions and their derivatives for those equations. We use the bibliographic reference of Butkov and Krantz for the development of the theoretical framework, Sabbah focuses the case on complex manifolds and Scardua-León on second and third order differential equations. To achieve the results we repeatedly use the inductive-deductive method and the handling of the indices for the series.