Differential Equation, Equalibrium

**Len** · January 27th 2010, 02:09 PM

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?

**nehme007** · January 27th 2010, 08:57 PM

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

**CaptainBlack** · January 27th 2010, 10:49 PM

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

Thread: Differential Equation, Equalibrium

LinkBack

Thread Tools

Display

Differential Equation, Equalibrium

Similar Math Help Forum Discussions

Transforming a differential equation into another differential equation

problem on matrix ricaati equation for nonlinear singular differential equation

Partial differential equation-wave equation(2)

Partial differential equation-wave equation - dimensional analysis

solve this Differential equation by indicial equation

Search Tags