As is clear from Figure gif, all solutions of with enter and remain in the backwards funnel between and as . That is,

for all t less than some negative constant . This inequality can be integrated from t to ; an argument identical to the one above then shows that


where is the time when enters the funnel. It can be shown [4, .6] that the solutions with (more generally all solutions lying above the curve in the left half-plane) become unbounded at a finite time ; such solutions are defined only for . Exercise.Use similar techniques to identify the behavior of solutions to , for any k>0.

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