Geodesic
Reduction of the Matier equation to a nonlinear first order one
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 66-69

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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 zone of the Mathieu equation describing the behavior of solutions not only inside this zone but also outside it. 
@article{VMUMM_2016_4_a11,
     author = {V. M. Budanov},
     title = {Reduction of the {Matier} equation to a nonlinear first order one},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {66--69},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/}
}
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V. M. Budanov. Reduction of the Matier equation to a nonlinear first order one. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 66-69. http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/