Equilibrium solutions of differential equations

Question

Being new to Mathematica, I'm not aware of all of the commands, etc. So, my apologies if this question is off base. In short; do you know if there is a "function/command" that finds Equilibrium points of a differential equation? i.e,;An equilibrium solution is a solution to a d.e. whose derivative is zero everywhere. One route; simplify and calculate the Derivitive and find the answer equal to 0 for each variable. But, is there a better route someone may be aware of?

Answer 1

I see no specific command. But why should it be. If your system is of the form

$\dot{x} = f[x[t]]$ --- the system is necessarily autonomous ---, the equilibria are given by

  sol = Solve[f[x]== 0, x] 

x scalar or vector