Regular singular point of non-linear ODE: $dot{x}(t) + t^{-1}Ax(t) = Q(x(t))$

Consider a system of ordinary differential equations of the form
$$
dot{x}(t) + frac{1}{t}Ax(t) = Q(x(t))
$$
where $x(t) in mathbb{C}^n$, $A in mathrm{Mat}_{ntimes n}(mathbb{C})$ is a constant matrix, and $Q: mathbb{C}^n to mathbb{C}^n$ is homogeneous of degree $2$, i.e. $Q(lambda x) = lambda^2 Q(x)$ for $lambda in mathbb{C}$.

What is known about existence of solutions near $t = 0$?

If it were not for the quadratic term $Q$, the point $t = 0$ would be a regular singular point of the ODE and then we could use the Frobenius method. But in all the references I know, regular singular points are only discussed for linear systems.