© 2024, Wilmington Scientific Publisher. All rights reserved.We consider analytic perturbations of quadratic homogeneous differential systems having an isolated singularity at the origin. Here we characterize the analytically integrable perturbations of quadratic homogeneous systems of the form (?, ?)T = f1(P1, Q1)T with f1(x, y) a non-zero linear homogeneous polynomial and P1(x, y), Q1(x, y) non-zero linear homogeneous polynomials without common factors. We prove that all systems are orbitally equivalent to their quasi-homogeneous leading terms with respect to a certain type but not necessarily to the homogeneous leading terms. This result completes the previous results for the analytic perturbations of irreducible quadratic systems with analytic first integral which are orbitally equivalent to the homogeneous leading term, i.e. all are homogenizable.