2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56589An algorithm for solving first order ODEs, by systematically determining symmetries of the form [ xi = F(x), eta = P(x) y + Q(x) ], where xi d/dx + eta d/dy is the symmetry generator - is presented. To these {\it 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 {\it always} exist but the algorithm will succeed in finding them only partially.13 pages. Submitted to European Journal of Applied Mathematics, July 2000. Related Maple programs are available at http://lie.uwaterloo.ca/odetools.htmMathematical PhysicsGeneral Mathematics34G20text