  In this paper we present a short material concerning to some results in
Morales-Ramis theory, which relates two different notions of integrability:
Integrability of Hamiltonian Systems through Liouville Arnold Theorem and
Integrability of Linear Differential Equations through Differential Galois
Theory. As contribution, we obtain the abelian differential Galois group of the
variational equation related to a bi-parametric Hamiltonian system,
