Generalized converted transformations and integrability in the quadrature of some classes of systems: Mikhail Israilovich

Uniform two -dimensional systems of linear differential equations with variable coefficients, as well as second -order equations with variable coefficients, are considered. A linear transformation of the desired functions is introduced, the coefficients of which satisfy the homogeneous linear system of differential equations, which is generalized to the initial system (or one second-order equation) containing some arbitrary function. In the case when this function can be selected in such a way that a generalized-consolidated system (equation) has a solution in quadrature or, in particular, in a clear analytical form, the original system (or equation) is also integrated in quadrature. A number of examples of cases of integrability in the quadrature of systems and equations are given.

Author
Israilovich Mikhail Yakovlevich
Publisher
Satellite+, 2015