Consider the system
$$x'=y$$ $$y'=x+x^2+\mu x-xy$$
we know that
$\operatorname{det}(Df(0,0))=-1$, then there is a saddle at the origin. In addition det $(Df (-1,0)) = 1> 0$, so there is a focus or a node at $(-1,0)$.
I need to do a translation from the origin to the point $(-1,0)$, when $ \mu = -1 $, this being how the new system would look?