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## Homework Statement

The following is part of a solution to a problem about finding equiblirum points of a differential equation and sketching its bifurcation diagram

http://img32.imageshack.us/img32/9194/63226925.jpg [Broken]

How did they get [itex]y= -1 \pm \sqrt{1- \mu}[/itex]?

## Homework Equations

The quadratic equation:

[itex]\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/itex]

## The Attempt at a Solution

Setting the DE equalt to 0:

[itex]\frac{dy}{dt} = \mu +2y+y^2 = 0[/itex]

Using the quadratic formula:

[itex]y = \frac{-2 \pm \sqrt{4-4 \mu}}{2}[/itex]

[itex]= -1 \pm \frac{\sqrt{4-4 \mu}}{2}[/itex]

So how did they get that answer? Any explanation is appreciated.

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