I frequently encounter in the literature the statement that Abel's equation $$\frac{dy}{dx}=x+y^3$$ is not integrable. This is always stated without reference. My questions are
a) What is the precise statement? (I suppose it should be that there is no non-constant meromorphic function (first integral) $F(x,y)$ on $C^2$ which is constant on each solution $y(x)$).
b) Where is this proved?
When I search in the reference books or internet, they list many known cases of integrability of Abel's equations, but no one addresses proofs of non-integrability.