Necessary and Sufficient Conditions for Finite Time Singularities in Ordinary Differential Equations

This paper gives a theorem which provides necessary and sufficient conditions for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equations diverges to infinity. This class is a large subset of the set of all autonomous, non-linear polynomial ordinary differential equation. These conditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically