Unravelling the Difference Between y' = sin(y) and y' = 2 + sin(y)

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The discussion focuses on the differences between the differential equations y' = sin(y) and y' = 2 + sin(y). The user utilized the Converge tool to visualize the equations and noted that adding a constant shifts the graph, resulting in steeper slopes. Specifically, it was concluded that while the graph appears to be rotated or translated, the primary effect is an increase in the slopes, leading to a lack of equilibrium solutions beyond y = sin(y) + 1. This understanding clarifies the behavior of the equations in terms of their graphical representation.

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epheterson
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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?
 
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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
 

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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.
 
I understand completely now, thanks
 

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