Numerical Approximations - Euler's Method

[theBEAST]

Homework Statement

Here is the problem

The Attempt at a Solution

I was able to draw the directional field and found which regions had a positive or negative slope. However I don't get what the question means by "Observe that there is a critical value of α in the interval 0 ≤ α ≤ 1 that separates converging solutions from diverging ones". What are converging and diverging solutions?

Additional hints are welcome :)

 

[HallsofIvy]

Looking at your direction field, you should be able to see that some of the arrows seem to be going "together" while others are going "apart". The first are "converging" and the second "diverging". There should be some specific curve separating them.