On the First Integrals of the Generalized Abel Equation of the Second Kind of Special Form
The study of various mathematical models described by nonlinear systems of differential equations, in many cases by special transformations reduces to the study of some nonlinear ordinary differential equations. In this article, the subject of such reduction and research is Abel equation of the second kind. Under certain assumptions on the coefficients of the equation construct the general solution of the generalized Abel equation of the second kind of special form.
1. Kamke E. Spravochnik po Obyknovennym Differentsial'nym Uravneniyam [Handbook of Ordinary Differential Equations]. Moscow, Nauka, 1971. 576 p.
2. Zaitsev V.F., Polyanin A.D. Spravochnik po Obyknovennym Differentsial'nym Uravneniyam [Handbook of Ordinary Differential Equations]. Moscow, FIZMATLIT, 2001. 576 p.
3. Semenov E.I. Properties of the Fast Diffusion Equation and its Multidimensional Exact Solutions. Sib. Math. Jour., 2003, vol. 44, no. 4, pp. 862-869.
4. Semenov E.I. New Exact Solutions of the Non-Autonomous Liouville Equation. Sib. Math. Jour., 2008. vol. 49, no. 1, pp. 207-217.
5. Rudykh G.A, Semenov E.I. The construction of exact solutions of one-dimensional nonlinear diffusion equation by the method of linear invariant subspaces. (in Russian). Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya «Matematika», V.6, №4, P. 69-84.
6. Appell P. Sur les Invariants de Quelques Equations Differentielles. Journal de Math. 1889, vol. 5, no. 4, pp. 361-423.
7. Lazhar Bougoffa. New Exact General Solutions of Abel Equation of the Second Kind. Appl. Math. and Comput., 2010, vol. 216, no. 2, pp. 689-691.