# Topology equivalence in dynamical system

#### erich22

Hi, my name is Eric.

I've got trouble when proofing that system
$$\displaystyle \dot{x}=\alpha+x^2+O(x^3)$$ is topological equivalence with system $$\displaystyle \dot{x}=\alpha+x^2$$.
I don't understand how to build the homeomorphism for the orbit.
In literature, I read that for $$\displaystyle \alpha>0$$, the homeomorphism mapping is defined by $$\displaystyle h_\alpha(x)=x$$, whereas when $$\displaystyle \alpha<0$$ define $$\displaystyle h_\alpha(x)=a(\alpha)+b(\alpha)x$$.

What is the function $$\displaystyle a(\alpha) \text{ }b(\alpha)$$ explicitly?