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 thatwhere 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.