Algebraic General Solutions of Algebraic Ordinary Differential Equations

J. Aroca, J. Cano, R. Feng, X. Gao


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.