A Polynomial Time Algorithm to Find Rational General Solutions of First Order Autonomous ODEs
نویسندگان
چکیده
We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order autonomous ODE F = 0, we give an exact degree bound for its rational solutions, based on the connection between rational solutions of F = 0 and rational parameterizations of the plane algebraic curve defined by F = 0. For a first order autonomous ODE, we further give a polynomial time algorithm to compute a rational general solution if it exists based on the computation of Laurent series solutions and Padé approximants. Experimental results show that the algorithm is quite efficient.
منابع مشابه
A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs
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