Abstract
In this paper we deal with differential equations of the form yy′ = P(x, y) where y′ = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions.
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Acknowledgement
The authors want to thank the referee for his/her valuable comments, that helped improving the paper.
The authors are partially suported by FEDER-MINECO grant MTM2016-77278-P, and a MINECO grant MTM2013-40998-P. A. Ferragut is also partially supported by the Universitat Jaume I grant P1-1B2015-16. J. Llibre is also partially supported by an AGAUR grant number 2014SGR-568.
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Ferragut, A., Llibre, J. On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn. Indian J Pure Appl Math 51, 217–232 (2020). https://doi.org/10.1007/s13226-020-0396-6
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DOI: https://doi.org/10.1007/s13226-020-0396-6
Key words
- Polynomial differential equation
- polynomial solution
- linear differential equation
- Riccati differential equation
- Abel differential equation