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Differential equation: Autonomous equation question

  1. Nov 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Screen Shot 2015-11-13 at 2.38.20 PM.png
    I'm stuck on Question #2 part A/B
    2. Relevant 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


    3. 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)
     
  2. jcsd
  3. Nov 13, 2015 #2

    epenguin

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    Homework Helper
    Gold Member

    Forget y'' - you only need to think about y'
     
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