Fritz Schwarz GMD, Institut SCAI 53754 Sankt Augustin, Germany Email: fritz.schwarz@gmd.de The Janet bases for the determining system of any 2nd order ordinary differential equation (ode) are completely classified. This is achieved by applying a general point transformation to the Janet bases for the various symmetry groups in canonical form and reestablishing the Janet base property afterwards. In this way for any given ode characteristic features of its Janet base are identified that areuniquley attached to this equation like a fingerprint. Asanapplication a decision procedure is described for determining the type of the symmetry group of a 2nd order ode from its Janet base. For the projective symmetry group a fast criterion in terms of the coefficients of the equation itself is given. The importance of these results for designing solution algorithms for nonlinear ode’s is pointed out. This is illustrated by numerous examples.
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