How to determine the stability of an ODE

I have been struggling with this for over 2 hours and nothing seems to work, some points that hinder me are - if y* is a critical point, and thus the derivative is 0, then the derivative of the derivative is also automatically 0, so how can it me smaller then 0 according to statement a? - how can i prove stability if i dont know the function? this surely has to be different for every function and the method I know is for known functions only. It would be a great help if someone could provide some answers, thanks

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  • hey im sorry i dont really know how this works, i am a student and someone reddit advised to post my question here.

  • The offered bounty should be high enough to give users incentive to spend time on answering your question. I believe $10 may be a fair bounty for this question.


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