I would appreciate if someone could please help me clarify this problem.
Given the system of equations $\frac{dx}{dt}=-4x+y+x^2$, $\frac{dy}{dy}=\frac{3}{2}\alpha-y$, where $\alpha$ is an arbitrary constant, we can find the two steady solutions to be: $(2+\sqrt{4-\frac{3}{2}\alpha}, \frac{3}{2}\alpha)$ and $(2-\sqrt{4-\frac{3}{2}\alpha}, \frac{3}{2}\alpha)$.
Now I need to perturb the steady solutions but I'm completely lost here since I don't know what exactly needs to be achieved. Does one remove square roots via perturbation or what? The aim is to then linearize the system with the perturbed steady solutions.