Let a system of the ordinary non-linear differential equations of the second order be a system of the linear algebraic equations with respect to the second derivatives. The set S where the principal determinant vanishes we call the singular set. We suppose that the system is defined on the set Γ and the first integral can be continuously prolongated on Γ ∪ S. The prolongation of the integral curve from Γ on Γ ∪ S, compatible with the prolongation of the first integral, is defined and studied in the case of mes S = 0 with respect to the Lebesgue measure.