Slope Field

  • Thread starter epheterson
  • Start date
  • #1
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Main Question or Discussion Point

You might want to use converge to help me out with this one, or maybe you know off the top of your head.

I'm trying to determine how

y' = sin(y)

is different from

y' = 2 + sin(y)


I plotted them both in Converge and I don't understand how adding a two rotated and skewed the graph.

Can you explain to me however possible what is going on here?
 

Answers and Replies

  • #2
22
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Or check out the attachment, I watched it while adding increments of .5 until I got up to y'=sin(y) + 2

It seems like every time you add a greater number, you increase the slope a little more. And past the point of y=sin(y) + 1, there are no more equilibrium solutions, it becomes monotonous.


Help?

I attached a word document with all the graphs from Converge
 

Attachments

  • #3
287
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Well, think about it.

It will rotate it because every slope becomes steeper, correct? Slopes that were 1 are now 3. That's a significant rotation.

It's looking translated is probably a coincidence. What really happened was an increasing of the slopes... and not a uniform one, at that.

So it's not really rotating or translating, although the periodicity of the field and the and the odd field transformation is making it look like that.
 
  • #4
22
0
I understand completely now, thanks
 

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