Polynomial Riccati equations with algebraic solutions
Volume 58 / 2002
Banach Center Publications 58 (2002), 219-231
MSC: Primary 12H05; Secondary 34C05, 58F21
DOI: 10.4064/bc58-0-17
Abstract
We consider the equations of the form $\frac{dy}{dx}=y^{2}-P(x)$ 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.
