Construction of Approximate Solution of One Nonlinear Differential Second-Order Equation in the Neighborhood of Movable Singular Point

Differential equations are mathematical models of various processes and phenomena. In contrast to linear, the nonlinear differential equations have been poorly studied. Difficulties in the study of nonlinear differential equations are associated with movable singular points. The method to solve approximately a nonlinear differential equation with movable singularities comprising the decision of six problems, is proposed. First two problems - theorem of existence and uniqueness of solutions of nonlinear differential equations as well as construction of approximate solutions and study of the initial condition perturbation influence on the approximate solution, are considered. Proof of the theorem of the solution existence and uniqueness of this nonlinear differential equation in the neighbourhood of movable singular point, and the approximate solution structure, are given.

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