I am working through an example to draw a phase diagram the DE used is $\frac{dx}{dt}=xy(x-1)(x-y)$
In the first step I have to identify the isoclines by setting $\frac{dx}{dt}=0$ having done this I found $x=0, y=0, x=1$ and $y=x$ this is obviously the $x$ axis, $y$ axis, a horizontal line $x=1$ and a line through the origin with slope 1
In the next step I am to identify the sign on both sides of this lines and insert direction arrows but I do not understand how to do this, and in the solution the line $y=x$ is not included. Any assistance please.