🚀 go-pugleaf

Hi netters.  I have a "simple" question about the asym. stability of a  
differential inequality.  Suppose a differential EQUATION
                 y_dotdot+a*y_dot+b*y=0     (y_dot=dy/dt, etc)
is asym. stable, i.e. y(t)->0 as t->infinity.  Now is the solution of
                 y(y_dotdot+a*y_dot+b*y)<0
which is equivalent to
                 y_dotdot+a*y_dot+b*y<0      if y>0
                 y_dotdot+a*y_dot+b*y>0      if y<0
also asym. stable?  My hunch is YES and it is bounded by the solution of
the aforementioned differential EQUATION.  But how to prove it or is it all
wrong?  Any help is greatly appreciated.  Please e-mail me.  Thanx.

Fengxi Zhou