Reduction of the Mathieu Equation to a Nonlinear Equation of the First Order / V. M. Budanov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 4. P. 66-69 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 98-101].

A second order equation with periodic coefficients is considered. It is shown that its analysis can be reduced to the study of a nonlinear equation of the first order. The second approximation is obtained for the first resonance region of the Mathieu equation. This approximation describes the behavior of solutions inside this resonance region and near it.

Key words: parametric resonance, equation with periodic coefficients.