If the differential equation isn't autonomous, then it presumably doesn't have any equilibria, as the rates of change would be explicitly changing with time. None of this analysis would apply.
In this case, you can directly calculate that y(t)=1 is a solution to the differential equation, at least if you start with a positive t. For y larger than 1, y' is clearly positive. For y smaller than 1, y' is clearly negative. Hence, nearby solutions are moving away from the solution y(t)=1.
![เจ็บที่ยังฮัก - ม่อน วรวิทย์ [ Official Mv ] จอนนี่มิวสิค](http://i.ytimg.com/vi/KALIGSRSjFs/mqdefault.jpg)
Super thanks! People who selflessly spare time and effort to help sc****d students like us restore faith in humanity... God bless you...
Thank you, this is such a great video, you actually explain it way better than my teacher
thanks , it was great. I choose dynamical system for degree, coz of u
what makes the differential equation semi-stable?
Thanks for your video! Very clear and easy to understand :)
Awesome video. Thank you
Thank you...concise and clear
I can not understand that how the arrow moves away or toward from origin. In which function do you ask ?
thanks i understood it all
great video man
What if it's not an autonomous differential equation?
If the differential equation isn't autonomous, then it presumably doesn't have any equilibria, as the rates of change would be explicitly changing with time. None of this analysis would apply.
What about an equation like:
y' = (y-1)/(t^2)
Would it be ok to just set y' = 0 and get rid of the t^2?
In this case, you can directly calculate that y(t)=1 is a solution to the differential equation, at least if you start with a positive t. For y larger than 1, y' is clearly positive. For y smaller than 1, y' is clearly negative. Hence, nearby solutions are moving away from the solution y(t)=1.