ordinary differential equation, Cauchy problem, moving singularity, perturbation, approximate solution, error estimation.

The article considers a first-order nonlinear ordinary differential equation with moving singularity which cannot be solved in quadratures in general case. The proof of the existence and uniqueness theorem for the solution of this equation in some neighborhood of moving singularity is provided. The approximate solution of the equation in neighborhood of moving singularity is constructed and research of influence of perturbation of moving singularity on the approximate solution is carried out. The results obtained in the complex domain are accompanied by calculations.

1. Orlov, Victor Nikolayevich Dr. of Phys. & Math. Sci., Professor, I. Yakovlev Chuvash State Pedagogical University, Cheboksary

2. Leonteva, Tatyana Yorevna Post-graduate Student, Department of Algebra, I. Yakovlev Chuvash State Pedagogical University, Cheboksary