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On the integrable rational Abel differential equations
Zeitschrift für angewandte Mathematik und Physik, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giné, Jaume, Llibre, Jaume
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Numerical Approach of Fractional Abel Differential Equation by Genocchi Polynomials
International Journal of Applied and Computational Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fariba Rigi, Haleh Tajadodi
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Algebraic geometry of Abel differential equation
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012Consider a system of differential equations \[ \dot{x}= -y + F(x,y), \qquad \dot{y}=x+G(x,y), \tag{\(*\)} \] where \(F\) and \(G\) are analytic functions without constant and linear terms. This system has a center at the origin if all the solutions around the origin are periodic.
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Functions Which Satisfy Abel’s Differential Equation
SIAM Journal on Applied Mathematics, 1967(4) 4)13 + (P23 + 033 30)10203 = 1. The addition formulae and other properties have been given in recent times by Silberstein [1], Oniga [2] and Bruwier [3], [4], while Mikusinski [5], [6] and Poli [7], [8] have studied the corresponding third order circular functions. Earlier workers in this field were Appell [9], Glaisher [10] and Villarceau [11]. It
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Rational solutions of Abel trigonometric polynomial differential equations
Journal of Geometry and Physics, 2022This paper deals with the trigonometric polynomial differential equations of the form \[ Y' = A(\theta) Y^2 + B(\theta) Y^3, \] where \(A\) and \(B\) are real trigonometric polynomials with \(B(\theta) \not\equiv 0\). This paper proves that these equations have at most two trigonometric polynomial solutions, and further shows that such solutions are ...
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