For planar autonomous systems * = f(x) (1) Assume that the origin is the unique singularity of the system, and it is stable, and there is no closed orbit or singular closed orbit in the whole plane, and try to prove: (i) Any trajectory of the system must be negative and unbounded; (ii) Any bounded positive half orbit must enter the singularity; (2) if the system is a linear system, whether the system may exist limit cycles is discussed in detail