  Let $dx_i/dt=f_i(x_1,\cdots,x_n)$, ($i=1,\cdots,n$) 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
$\Phi(t,x_1,\cdots,x_n)=(\varphi_0(t),\varphi_1(x_1),\cdots,\varphi_1(x_1))$.
