# Seeking help: the direction field are all vertical bars

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ryecatcher on 13 Feb 2020
Commented: ryecatcher on 13 Feb 2020
Dear All:
First of all, I am sorry for the newbie questions. I have googled everywhere, including you-tube, and still cannot get my direction field correctly.
I am trying to plot the direction field of this differential equation: dy/dt=y*(y-1)(y-2)
Clearly, there are 3 critical points. y=0 & 2 are unstable; y=1 is stable.
My code:
% y'=y(y-1)(y-2)
[T, Y]=meshgrid(-3:0.1:3, -3:0.1:3)
S=Y*(Y-1)*(Y-2);
L=sqrt(1+S.^2);
quiver(T, Y, 1./L, S./L, 0.3), axis tight
xlabel 't', ylabel 'y'
title 'Direction Field for dy/dt = y(y-1)(y-2)'
Below is what I got. I don't understand why most part are just vertical bars. I cannot see the trend at all. I have played with changing some parameters in the code and it still didn't come out nicely. Thank you very much for your help. I greatly appreciate it. darova on 13 Feb 2020
YOu forgot the dot
S = Y.*(Y-1).*(Y-2);
Don't you forgot dt here?
L=sqrt(1+S.^2);
ryecatcher on 13 Feb 2020
Dear Sir: Thank you very much for your reply! Following your suggestion, now it has worked. I have added dot at two places:
previous wrong code:
S=Y*(Y-1)*(Y-2);
Now, the correct working code:
S=Y.*(Y-1).*(Y-2);
Here is the direction field picture. y=0, 1 and 2 are equilibrium solutions. y=1 is stable 