, 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.
![[Annotate]](/organics/icons/sannotate.gif){kind=icon}
![[Shownotes]](../gif/annotate/shide-111.gif)