Numerical Approximations - Euler's Method

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The discussion focuses on understanding the concept of converging and diverging solutions in the context of Euler's Method and directional fields. A critical value of α exists within the interval 0 ≤ α ≤ 1 that distinguishes between these two types of solutions. Converging solutions are represented by arrows in the directional field that move towards each other, while diverging solutions are indicated by arrows moving apart. Identifying the specific curve that separates these solutions is essential for solving the problem. Additional hints suggest that analyzing the directional field will clarify the behavior of the solutions.
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Homework Statement


Here is the problem
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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 :)
 
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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.
 

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