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## Homework Statement

What are the bifurcation values for the equation:

dy/dt = y^3 +ay^2

## Homework Equations

## The Attempt at a Solution

Equilibrium solutions:

y^3 + ay^2 = 0

==> y^2 (y + a) = 0

==> y = 0 (double root), or y = -a.

a = 0 is the sole bifurcation point, since

a < 0 ==> two equilibrium solutions

a = 0 ==> one equilibrium solution

a > 0 ==> two equilibrium solutions.

my question is how can you tell that a < 0 has two equilibrium solutions and a=0 has one and a>0 has two again?