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

[epheterson]

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?

 

[epheterson]

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

 

[csprof2000]

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.

 

[epheterson]

I understand completely now, thanks