By a classical formula due to Enriques, the Euler number χ(X) of the non-singular normalization X of an algebraic surface S with ordinary singularities in P³(ℂ) is given by χ(X) = n(n²-4n+6) - (3n-8)m + 3t - 2γ, where n is the degree of S, m the degree of the double curve (singular locus) $D_S$ of S, t is the cardinal number of the triple points of S, and γ the cardinal number of the cuspidal points of S. In this article we shall give a similar formula for an algebraic threefold with ordinary singularities...

Dans cet article, nous étudions le problème de l’existence de polynômes de Darboux dans $\mathbf{C}\left\{x\right\}\left[y,y^{\prime }\right]$ pour la dérivation $\delta =R\left(y\right){\partial }_x+R\left(y\right)y^{\prime }{\partial }_y-V(y,y^{\prime }){\partial }_{y^{\prime }}$.