1. ## Differential Equation, Equalibrium

Consider the Differential Equation

$\frac{dy}{dt}=2*\sqrt{|y|}$

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 $2*\sqrt{|0|}=0 ?$ for all t because it depends on y?

2. 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 ( $\frac{dy}{dx} = f(y)$).

Check here for a more thorough description: Pauls Online Notes : Differential Equations - Equilibrium Solutions

3. Originally Posted by Len
Consider the Differential Equation

$\frac{dy}{dt}=2*\sqrt{|y|}$

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 $2*\sqrt{|0|}=0 ?$ for all t because it depends on y?
No, an equilibrium solution is one that is unchanging, so $y'(t)=0$ for all $t$. In this case this gives:

$2\sqrt{|y|}=0$

and the rest you know.

CB