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Is there a simple proof of the existence and uniqueness of a solution of [itex]x''(t)=f(x'(t),x(t),t)[/itex], where f is an appropriately "nice" function? (Given an initial condition [itex]x(t_0)=x_0,\ x'(t_0)=v_0[/itex], or a boundary condition [itex]x(t_0)=x_0,\ x(t_1)=x_1[/itex]).