Okay, I have the following autonomous differential equation:
I found the steady states of the equation of be x*1=2 and x*2=3
When I sub them into , I get and .
Now I was told that the stability theorem states that if , then x* is stable and when , x* is unstable, however, when I create my phase line diagram is shows that x*2 is stable.
Could someone shed some light on this?
I also have another part of the question I need help with:
It asks to use separation of variable to determine the equation explicitly, however when I integrate it, I get an equation that doesn't make sense:
I separated the variables to get an equation with which I needed to use integration by parts. I determined that A=1 and B=-1 to which i got the final equation to be
Taking the e function to everything and simplifying got me that. Could there have been a mistake in my integration (I apologize, I'm not too familiar with the math functions on this site so I wasn't able to show you what I did).