Seeking help: the direction field are all vertical bars

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.

Answer 1

[darova]

YOu forgot the dot

S = Y.*(Y-1).*(Y-2);

Don't you forgot dt here?

L=sqrt(1+S.^2);

[ryecatcher]

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