Matlab plotting direction field, stable or unstable?

I'm trying to figure out which equilibrium solutions are stable and unstable for this differnetial equation (Gompertz model) y'=y(1-ln(y)(y-3), so here is my code:

%%-----------------------------------------------------------

[y]=solve('y*(1-log(y))*(y-3)=0'); % solving for the equilibrium solution

disp('The Equilibrium solutions are y=') 
y
% plotting the direction field 
figure, hold on 
syms t c 
[T Y]= meshgrid(0:.5:12, -5:.5:12);
S= Y.*(1-log(Y)).*(Y-3);
L=sqrt(1+S.^2);
quiver(T, Y, 1./L, S./L, 0.5), axis tight
xlabel 'S', ylabel 'y'
hold off 

%%-----------------------------------------------

however the graph it self is sort of ambiguous, i am having difficulty "reading the direction field" from about 2.5 and 3- there appears to be a continuous of equilibrium solutions.

Does anyone have any idea as to why the graph appears to be inconclusive on this interval?

I tried to graph the function and I found the limit as the function went to zero, and I found that it was 0. But I still am not sure why it appears this way. I think maybe the maximum value of f(y) has to something to do with it?

%--------------------------------

% code for graphing f(y) and finding the limit:
clear all 
f=@(y) (y.*(1-log(y)).*(y-3));
Y=0:.1:4;
Z=f(Y);
plot(Y,Z)
title 'Plot of y.*(1-log(y)).*(y-3)'
xlabel y
ylabel f(y) 

syms y 
limit(y*(1-log(y))*(y-3),y,0)