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  • @phdthesis{RISC4390,
    author = {L.X.C. Ngo},
    title = {{Rational General Solutions of First-Order Algebraic ODEs}},
    language = {english},
    abstract = {Solving algebraic ordinary differential equations (AODEs) has been of interest for a long time and is still an active topic of research. Several classical AODEs have been studied by different methods. It is natural to see them in a bigger class, in which all the equations can be treated uniformly. In this Ph.D. thesis we present an algebraic geometric method to determine the existence of a rational general solution of a parametrizable first-order AODE; if the answer is yes, we will find such a general solution. Our method is based on a rational parametrization of a rational algebraic surface, obtained by neglecting the differential aspect of the differential equation, and on the degree bound of a rational general invariant algebraic curve of the associated system derived from this parametrization. This approach enables us to treat a wide class of parametrizable first-order AODEs in a uniform way.},
    year = {2011},
    month = {October},
    translation = {0},
    school = {Research Institute for Symbolic Computation (RISC)},
    length = {88},
    type = {RISC Technical Report 11-12}
    }