Conditional closed-form solutions for extended Liénard equations are obtained via Abel reduction and Chiellini-type conditions, with one theorem containing a mathematical error.
Generalized damped Milne-Pinney equation and Chiellini method
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abstract
We adopt the Chiellini integrability method to find the solutions of various generalizations of the damped Milne-Pinney equations. In particular, we find the solution of the damped Ermakov-Painlev\'e II equation and generalized dissipative Milne-Pinney equation.
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On the integrability of the Abel and of the extended Li\'{e}nard equations
Conditional closed-form solutions for extended Liénard equations are obtained via Abel reduction and Chiellini-type conditions, with one theorem containing a mathematical error.