On integrability of nonautonomous system of ordinary differential equations applied in dynamic theory of elasticity

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.