nonlinear differential equation of the second order, a movable singular point, approximate solution, perturbation of the movable singular point, the exact criteria for the existence of the solution.

The nonlinearity of the differential equation is manifested in the appearance of movable singular points, to find which requires a certain mathematical apparatus. And this task is part of a method for the approximate solution of nonlinear differential equations with movable singularities. Recently these tasks were considered for several classes of nonlinear differential equations. The results of this work extend the class of nonlinear differential equations with movable singularities.

Leont’eva, Tat’jana Jur’evna, Postgraduate Student, Department of Mathematical analysis, Algebra and Geometry, I. Yakovlev Chuvash State Pedagogical University, Cheboksary, Russia.