Chiellini-Integrable Cosmologies with Phantom Divide Crossing

We investigate exact cosmological solutions with a massive scalar field minimally coupled to the Einstein-Hilbert action in General Relativity. For an extended Higgs-like scalar self-interaction, we find that the resulting field equations belong to the damped Ermakov-Painlev\'e II class and construct novel analytical solutions within the framework of the Chiellini integrability condition. We analyze whether the expanding branch of the solutions can describe a late-time cosmic acceleration, using a combined statistical analysis of BAO, CMB, cosmic chronometer and Pantheon+SHOES supernova datasets. A crucial outcome of this exercise is the analytical emergence of a smooth phantom divide crossing in the dark energy equation of state, achieved without introducing any pathological instabilities. The reconstruction yields a present-day Hubble parameter $H_0 \gtrsim 70 \,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, with a reduced tension relative to the $\Lambda$CDM cosmology. The results indicate that Chiellini-integrable scalar cosmologies are capable of providing a robust and analytically controlled framework for modeling late-time cosmic acceleration and phantom divide crossing, offering a viable alternative to phenomenological dark-energy parametrizations.