Alternative methods of integrability of nonlinear ordinary differential equations of the first order with polynomial part
UDC
517.54EDN
UPGTXZDOI:
10.31429/vestnik-16-2-6-14Abstract
Alternative methods of integrability of nonlinear ordinary differential equations of the first order with polynomial part. The method of research of integrability of the nonlinear differential equation of the first order with polynomial part, on the basis of introduction of parameters allowing to bring the initial equation to system of the differential equations which ways of integrability are known is developed in work. The equations connecting the parameters and coefficients of the original equation determining the conditions of integrability of the considered differential equation are composed. Integral and algebraic representations of solutions of differential equations are specified. The presented facts are structured by the method of gradualism: first, attention is paid to the equation with the polynomial of the second degree (Riccati equation), examples are given. Then the equation with a polynomial of the third degree is considered. Finally, we investigate a differential equation with a polynomial of any order.
Keywords:
analysis, geometric theory of functions of a complex variable, differential equationsReferences
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