Web geometry of a system of n first order autonomous ordinary differential equations

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Let dxᵢ/dt=fᵢ(x₁,,xₙ), (i=1,,n) be a system of n first order autonomous ordinary differential equations. We use E. Cartan's equivalence method to study the invariants of this system under diffeomorphisms of the form Φ(t,x₁,,xₙ)=(φ₀(t),φ₁(x₁),,φ₁(x₁)).