Analytical properties of the solutions of a fourth-order nonlinear ordinary differential equation
Introduction of the present article indicates the object of investigation: the fourth-order differential equation. The purpose of the research is to study the analytic properties of solutions of the equation considered. In the main part of the article the solution is constructed in the form of the Laurent series. The solutions in the form of Dirichlet series and exponential series with respect to fractional-linear functions have been formulated. The issues of the series convergence, which represent the solution of this fourth-order differential equation, have been explored. The existence of three-parameter solutions with a movable singular line has been established. The obtained results can be used in the analytical theory of ordinary differential equations.