@article{FENG2006739,
    Abstract = {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 parametrizations of the plane algebraic curve defined by F=0. For a first order autonomous ODE, we further give a polynomial time algorithm for computing a rational general solution if it exists based on the computation of Laurent series solutions and Pad{\'e} approximants. Experimental results show that the algorithm is quite efficient.},
    Author = {Feng, Ruyong and Gao, Xiao-Shan},
    File = {A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs - 1-s2.0-S0747717106000083-main.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Keywords = {Rational general solution, First order autonomous ODE, Rational parametrizations, Laurent series, Pad{\'e} approximants, Polynomial time algorithm},
    Number = {7},
    Pages = {739-762},
    Title = {A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs},
    URL = {https://www.sciencedirect.com/science/article/pii/S0747717106000083},
    Volume = {41},
    Year = {2006},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717106000083},
    bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2006.02.002},
    date-added = {2023-07-19 07:33:23 +0200},
    date-modified = {2023-07-19 07:33:23 +0200},
    doi = {10.1016/j.jsc.2006.02.002}
}

@article{FENG2006739, Abstract = {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 parametrizations of the plane algebraic curve defined by F=0. For a first order autonomous ODE, we further give a polynomial time algorithm for computing a rational general solution if it exists based on the computation of Laurent series solutions and Pad{\'e} approximants. Experimental results show that the algorithm is quite efficient.}, Author = {Feng, Ruyong and Gao, Xiao-Shan}, File = {A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs - 1-s2.0-S0747717106000083-main.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Keywords = {Rational general solution, First order autonomous ODE, Rational parametrizations, Laurent series, Pad{\'e} approximants, Polynomial time algorithm}, Number = {7}, Pages = {739-762}, Title = {A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs}, URL = {https://www.sciencedirect.com/science/article/pii/S0747717106000083}, Volume = {41}, Year = {2006}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717106000083}, bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2006.02.002}, date-added = {2023-07-19 07:33:23 +0200}, date-modified = {2023-07-19 07:33:23 +0200}, doi = {10.1016/j.jsc.2006.02.002} }