What is an example of an entire non constant holomorphic function $\gamma: \mathbb{C} \to \mathbb{C}P^2$ such that the image of $\gamma$ is a leaf of a singular holomorphic foliation of $\mathbb{C}P^2$ arising from a non linear polynomial vector field on $\mathbb{R}^2$ or $\mathbb{C}^2$?

Moreover, is it true to say that every leaf of a singular holomorphic foliation of $\mathbb{C}P^2$ is the image of an entire function defined on whole $\mathbb{C}$.

The above question is included in the following post but it did not get an answer. So I ask it as an independent question

The error in Petrovski and Landis' proof of the 16th Hilbert problem