The function represents a velocity field. That is, the equation is equivalent to find the movement of a particle in the real line such that its velocity in any instant of time is exactly . The arrows represent the movement sense. Hope this helps.
I understand how to create a horizontal phase line of a function...
...but I don't really understand what it means. What does the horizontal line represent and what do the arrows represent?
And what procedure would I use for answering the question:
The solution of the above equation with is defined on the interval , find
Is there a way to find the limit analytically? I'm guessing not since we're using the phase line to do it.