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!
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sunnewton wrote:

Homework?
--

Tim Wescott
Wescott Design Services
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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
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Nasser, Thanks a lot:)
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