Differential equation: Autonomous equation question

  • Thread starter Hutchyy
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Homework Statement


Screen Shot 2015-11-13 at 2.38.20 PM.png

I'm stuck on Question #2 part A/B

Homework Equations


y'=r(1-y/k)y-h=y^2-ky+kh/r
y''=2y-k
Roots for y'= (k+/-sqrt(k^2-4kh/r))/2 Im assuming the positive root is y2
h<rk/4
[/B]

The Attempt at a Solution


on part a I'm getting the roots to be y2=(K+sqrt(k^2-4kh/r))/2 and y1=(K-sqrt(k^2-4kh/r))/2... I then got the second derivative of the function to be y''=2y-k and when i plug in the equilibrium equations to check which one is stable and unstable I get for y2 that it is unstable and for y1 it's stable but I know that it should be the reverse... unless somehow y2 is less than y1. Or I'm mislead in thinking that y''<0 is stable and y''>0 is unstable (in question #1 that is how it seemed to work out)
 

Answers and Replies

  • #2
epenguin
Homework Helper
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Forget y'' - you only need to think about y'
 

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