ar X iv : m at h - ph / 0 00 70 23 v 1 1 5 Ju l 2 00 0 First order ODEs , Symmetries and Linear Transformations
نویسنده
چکیده
An algorithm for solving first order ODEs, by systematically determining symmetries of the form [ξ = F (x), η = P (x) y+Q(x)] where ξ ∂/∂x+η ∂/∂y is the symmetry generator is presented. To these linear symmetries one can associate an ODE class which embraces all first order ODEs mappable into separable through linear transformations {t = f(x), u = p(x) y + q(x)}. This single ODE class includes as members, for instance, 78% of the 552 solvable first order examples of Kamke’s book. Concerning the solving of this class, a restriction on the algorithm being presented exists only in the case of Riccati type ODEs, for which linear symmetries always exist but the algorithm will succeed in finding them only partially.
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ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications
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