By using a method proposed by Langer, we construct a formal solution of an integrodifferential equation obtained as a result of the asymptotic integration of a system of linear differential equations with a small parameter near a part of derivatives.
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A. N. Samoilenko, “On the asymptotic integration of a system of linear differential equations with a small parameter in the coefficients of a part of derivatives,” Ukr. Mat. Zh., 54, No. 11, 1505–1516 (2002); English translation: Ukr. Math. J., 54, No. 11, 1825–1841 (2002).
W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York (1965).
R. E. Langer, “The solutions of the differential equation ν″′ + λ 2 zν′ + 3μλ 2 ν = 0,” Duke Math. J., 22, 525–542 (1955).
E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Akademische Verlagsgesellschaft Geest, Leipzig (1959).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 421–426, March, 2011.
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Skutar, I. Construction of a solution of one integrodifferential equation. Ukr Math J 63, 487–493 (2011). https://doi.org/10.1007/s11253-011-0517-9
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DOI: https://doi.org/10.1007/s11253-011-0517-9