Ordinary differential equations of the 2nd and 3rd orders with multiplicative right-hand sides of the 2nd and 3rd orders are studied. A method is considered for reducing the order of equations and obtaining exact solutions of differential equations using transformations that are invariants of generators of cyclic transformations discrete groups closed in the classes of differential equations under consideration. The method of discrete invariants is an alternative to the method of "multiplication" of integrable cases in the class of differential equations under study by using the constructed discrete group of transformations acting in this class of equations. Examples are given to illustrate the method of discrete invariants.

Zilya Nailevna Khakimova

Integration of Differential Equations by Using Invariants of Discrete Transformation

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