Algebraic general solutions of algebraic ordinary differential equations

In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For an autonomous first order ODE, we give an optimized bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists.

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: J. M. Aroca, J. Cano, Ruyong Feng, Xiao-Shan Gao
• Keywords: Algebraic General Solution, Algebraic Ode, Autonomous first Order, ISSAC 2005