stability of (0,0) critical point

$ text {The critical point $ (0,0) $ for the system} $

$ x $ (t) $=$ x-2y + y ^ {2} sin (x) $

$ y & # 39; (t) $=$ 2x-2y-3y cos (y ^ {2}) $

$ text {is}}

  • $ text {stable spiral point} $
  • $ text {unstable spiral point} $
  • $ text {saddle stitch} $
  • $ text {stable point} $