2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163949This paper focuses on isochronicity of linear center perturbed by a polynomial. Isochronicity of a linear center perturbed by a degree four and degree five polynomials is studied, several new isochronous centers are found. For homogeneous isochronous perturbations, a first integral and a linearizing change of coordinates are presented. Moreover, a family of Abel polynomial systems is also considered. By investigations until degree 10 we prove the existence of a unique isochronous center. These results are established using a computer implementation based on Urabe theorem.26 pagesClassical Analysis and ODEs34C15, 34C25, 34C37text