Uniqueness of the solution of a system of differential equations unsolved for the derivatives (Q2577297)

For the system of equations \[ F_i\left(t,x_1,\dots,x_n,\frac {dx_1} {dt},\dots, \frac{dx_n}{dt}\right)=0,\;i=1,\dots,n, \] it is shown that the uniqueness of a solution with initial conditions at a nonsingular point depends on \(n\) and on whether solutions with discontinuous derivatives are admitted. Sufficient conditions for uniqueness are given.