ON THE SINGULARITY ANALYSIS OF ORDINARY DIFFERENTIAL-EQUATIONS INVARIANT UNDER TIME TRANSLATION AND RESCALING

The PT is applied to the general second- and third-order ordinary diff erential equations invariant under the two symmetries associated with time translation and rescaling in order to investigate their solvabili ty and global integrability. The effect of the two symmetries on the c ompatibility conditions is determined and we show that, generally. the se conditions are automatically a consequence of the resonance conditi on. Use is made of truncated Laurent series both in ascending and desc ending powers. As an example, the case of the generalized hazy equatio n is presented.