On the differential factorization method in problems for continuous media

A study was conducted, to apply the differential factorization method to boundary-value problems for continuous media. The factorization method was specifically applied to the dynamical problems of elasticity theory, as these problems were convenient for comparing different methods with their solution and demonstrate significant potentialities of the differential factorization method. These problems include cases, involving the main types of roots of the determinants of characteristic equations of the corresponding differential equations. A significant advantage of the factorization method is that it can be applied to boundary-value problems for various differential equations according to the same algorithm, despite different varieties of these equations.