Symbolic solution of nonhomogeneous linear ordinary differential equations in terms of power series

For a nonhomogeneous linear ordinary differential equation Ly(x) = f(x) with polynomial coefficients and a holonomic right-hand side, a set of points x = a is found where a power series solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$y(x) = \sum\nolimits_{n = 0}^\infty {c_n (x - a)} ^n $$ \end{document} with hypergeometric coefficients exists (starting from some number, the ratio cn + 1/cn is a rational function of n).