The stability of equilibria of a differential equation, analytic approach

[@lokidragion4859]

Thank you, this is such a great video, you actually explain it way better than my teacher

[@Taddius4zindagi]

Super thanks! People who selflessly spare time and effort to help sc****d students like us restore faith in humanity... God bless you...

[@shadenaguirre6317]

what makes the differential equation semi-stable?

[@viji001]

thanks , it was great. I choose dynamical system for degree, coz of u

[@ankit45822]

I can not understand that how the arrow moves away or toward from origin. In which function do you ask ?

[@Mr1Lemos]

Thanks for your video! Very clear and easy to understand :)

[@danieltian5088]

Awesome video. Thank you

[@robert6816]

Thank you...concise and clear

[@tomenart]

great video man

[@uditsaxena3844]

thanks i understood it all

[@Fabian_AD]

What if it's not an autonomous differential equation?

[@duanenykamp5700]

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.

[@Fabian_AD]

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?

[@duanenykamp5700]

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.