T. Harko, F. S. N. Lobo, M. K. Mak
Abstract
A class of exact solutions is obtained for the Liénard-type ordinary nonlinear differential equation. As a first step in our study, the second-order Liénard-type equation is transformed into a first Abel kind, first order differential equation. With the use of an exact integrability condition for the Abel equation (Chiellini lemma), the exact general solution of the Abel equation can be obtained, leading to a class of exact solutions of the Liénard equation, expressed in parametric form. We also extend the Chiellini integrability condition to the case of the general Abel equation. As an application of the integrability condition the exact solutions of some particular Liénard-type equations, including a generalized van der Pol–type equation, are explicitly obtained.
Keywords
Abel equation - Exact solutions - Integrability condition - Liénard equation
Journal of Engineering Mathematics
Volume 89, Number 1, Page 193
2014 December
