Consider the Differential Equation
Show that the function y(t)=0 is an equilibrium solution for all t.
Is this simply showing the derivative of 0 is 0 and then that for all t because it depends on y?
Consider the Differential Equation
Show that the function y(t)=0 is an equilibrium solution for all t.
Is this simply showing the derivative of 0 is 0 and then that for all t because it depends on y?
Yes. Equilibrium solutions are constant solutions to the differential equation. They can be found by simply setting the derivative equal to 0 and solving for the dependent variable. This is assuming you are looking at an autonomous differential equation, that is, one in which the independent variable does not appear ( ).
Check here for a more thorough description: Pauls Online Notes : Differential Equations - Equilibrium Solutions