TY - JOUR
T1 - On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n
AU - Ferragut, Antoni
AU - Llibre, Jaume
N1 - Publisher Copyright:
© 2020, Indian National Science Academy.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
KW - Abel differential equation
KW - Polynomial differential equation
KW - Riccati differential equation
KW - linear differential equation
KW - polynomial solution
UR - https://www.scopus.com/pages/publications/85081719192
U2 - 10.1007/s13226-020-0396-6
DO - 10.1007/s13226-020-0396-6
M3 - Article
AN - SCOPUS:85081719192
SN - 0019-5588
VL - 51
SP - 217
EP - 232
JO - Indian Journal of Pure and Applied Mathematics
JF - Indian Journal of Pure and Applied Mathematics
IS - 1
ER -