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ABSTRACT. The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, dcurvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given linear ODEs system or a given superior order ODE. The case of a non-homogenous linear ODE of superior order is discussed.Mathematics Subject Classification (2010): 53C43, 53C07, 83C22.

Keywords: 1-jet spaces, jet least squares Lagrangian functions, Riemann-Lagrange geometry, linear ODEs systems, superior order ODEs.