How to find equilibrium?????!!!

Dear All,

How to find the asymptotically equilibrium of the following nonlinear system

.. . y+(2+y) y-8y+y^2=0

I want to denote the equilibrium point as y0 and use the following Lyapunov candidate . V=1/2y^2+1/2 y^2

then how to handle?

Thanks in advance!

Homework?

Convert to 2 1st order ODE's as you would do when you build the A matrix for the state space formulation.

Then set the right hand side of these 2 equations to zero. Since at equilibrium, x1'=0 and x2'=0

You'll get 2 equations in 2 unknowns, the x1 and x2 (where x1=y, and x2=y')

And then solve these 2 algebraic equations for x1,x2, the state variables.

This gives you the set of points (x1,x2), which are the equilibrium points.

Nasser

Nasser, Thanks a lot:)