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SOME QUADRATURE INTEGRABLE FUNCTIONAL-DIFFERENTIAL EQUATIONS

Annotation

Some simple first order linear functional-differential equations integrable in quadrature are considered. For such equations, the general solution involving the Cauchy function is found.

Keywords

linear functional-differential equations; differential equations with delay; the Cauchy function; general solution

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UDC

517.929

Pages

1079-1083

References

1. Kamke E. Spravochnik po obyknovennym differentsial'nym uravneniyam. M.: Nauka, 1976. 576 s. 2. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Vvedenie v teoriyu funktsional'no-differentsial'nykh uravneniy. M.: Nauka, 1991. 280 s. 3. Vulikh B.Z. Kratkiy kurs teorii funktsiy veshchestvennoy peremennoy. M.: Nauka, 1973. 352 s. 4. Zhukovskiy E.S. Ispol'zovanie ryada Neymana dlya postroeniya funktsii Grina // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 1997. T. 2. № 2. S. 205–206. 5. Kim A.V., Pimenov V.G. i-Gladkiy analiz i chislennye metody resheniya funktsional'no-differentsial'nykh uravneniy. Izd-vo: Regulyarnaya i khaoticheskaya dinamika, 2004. 256 s. 6. Zhukovskaya T.V., Molokanova E.A. Chislennye metody resheniya evolyutsionnykh funktsional'no-differentsial'nykh uravneniy // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2012. T. 17. № 5. S. 1352–1359. 7. Zhukovskaya T.V. Interpolyatsiya funktsii Koshi // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2002. T. 7. № 1. S. 110–111. 8. Zhukovskaya T.V. Metod postroeniya funktsii Koshi uravneniya s obobshchenno vol'terrovym operatorom // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2003. T. 8. № 1. S. 162-163.

Received

2015-06-02

Section of issue

Scientific articles

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