A variant of the approximate solution of nonlinear differential equation of the third order in the neighborhood of a movable singular point

This paper considers one class of nonlinear differential equations in the General case, unsolvable in closed form, requiring the solution of the problem of finding an analytical approximate solution in the neighborhood of a movable singular point. This problem is successfully solved based on the new approach, the majorant method in the proof of a theorem of existence and uniqueness of the solution. Accounting a posteriori error estimate allows to improve the a priori error estimate for the approximate analytical solution and optimize the structure of the approximate solution.