A Combinatorial Problem in the Classi cationof Second - Order Linear ODE ' sBruno
نویسندگان
چکیده
We study a problem of classiication of linear homogeneous second-order ODE's with polynomial coeecients based on qualitative properties of singularities. The corresponding combinatorial problem of counting the number of classes is then solved in terms of the initial number of singularities. Un probl eme combinatoire en classiication des EDO lin eaires du second ordre R esum e Nous etudions un probl eme de classiication d' equations lin eaires homog enes du second ordre a coeecients polynomiaux fond ee sur des propri et es qualitatives des singularit es. Le probl eme combinatoire consistant a compter le nombre de classes dans la classiication est ensuite r esolu en fonction du nombre initial de singularit es. Abstract We study a problem of classiication of linear homogeneous second-order ODE's with polynomial coeecients based on qualitative properties of singularities. The corresponding combinatorial problem of counting the number of classes is then solved in terms of the initial number of singularities.
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