Geodesic
On integrability of nonautonomous system of ordinary differential equations applied in dynamic theory of elasticity
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 117 (2008) no. 2, pp. 87-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article shows the possibility of generating new accurate solution of the system of two ordinary linear homogeneous differential second-order equations with variable general coefficients. It is essential that the integrability identifies its own functions of initial-boundary axisymmetric dynamic problem of theory of elasticity for anisotropic cylinder in the procedure of final integral transformational method. Special case that complies with the heterogeneous anisotropic cylinder is analyzed. During the research transformation of variable data combined with the method of factorization and introduction of inducing differential equations was used.
Keywords: nonautonomous ODE systems, dynamic problem of elasticity theory, anisotropic cylinder. 
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     title = {On integrability of nonautonomous system of ordinary differential equations applied in dynamic theory of elasticity},
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Yu. È. Senitskii. On integrability of nonautonomous system of ordinary differential equations applied in dynamic theory of elasticity. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 117 (2008) no. 2, pp. 87-93. http://geodesic.mathdoc.fr/item/VSGTU_2008_117_2_a9/

[1] Senitskii Yu. E., “K probleme integriruemosti osesimmetrichnoi kraevoi zadachi dinamiki dlya neodnorodnogo anizotropnogo konechnogo tsilindra”, Prikl. mekhanika, 35:4 (1999), 19–29 | MR

[2] Korenev B. G., Vvedenie v teoriyu besselevykh funktsii, Nauka, M., 1974, 287 pp. | MR

[3] Senitskii Yu. E., Epishkin V. V., “Dinamicheskaya zadacha teorii uprugosti dlya anizotropnogo korotkogo tsilindra s uchëtom sil vyazkogo soprotivleniya”, Izvestiya vuzov. Stroitelstvo, 2008, no. 3, 29–41