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.
Thank you, this is such a great video, you actually explain it way better than my teacher
Super thanks! People who selflessly spare time and effort to help sc****d students like us restore faith in humanity... God bless you...
thanks , it was great. I choose dynamical system for degree, coz of u
Thanks for your video! Very clear and easy to understand :)
what makes the differential equation semi-stable?
Awesome video. Thank you
I can not understand that how the arrow moves away or toward from origin. In which function do you ask ?
Thank you...concise and clear
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.