We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-17,
author = {Henryk \.Zo\l \k adek},
title = {Polynomial Riccati equations with algebraic solutions},
journal = {Banach Center Publications},
volume = {58},
year = {2002},
pages = {219-231},
zbl = {1025.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-17}
}
Henryk Żołądek. Polynomial Riccati equations with algebraic solutions. Banach Center Publications, Tome 58 (2002) pp. 219-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-17/