Rational General Solutions of Ordinary Differential Equations

Ru-Yong Feng and Xiao-Shan Gao
Key Laboratory of Mathematics Mechanization
Academy of Mathematics and System Sciences
Chinese Academy of Sciences, Beijing 100080, China


Abstract. We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order ODE with constant coefficients, we give a polynomial time algorithm to compute a rational general solution if it exists.