  In this work, we present a study on cosmological constraints of dark energy
parametrizations post-DESI 2024, suggesting potential deviations from the
standard $\Lambda$CDM cosmology. This study aims to put observational
constraints on EoS parametrizations beyond the standard $\Lambda$CDM model
using DESI BAO 2024 data, CMB anisotropy observations 2018, and various
Pantheon+, Union 3, and DES 5YR SNIa compilations. Our main goal is to check
the result of DESI collaborations \cite{DESI:2024mwx} in the context of some
generalizations of CPL approximation known as BA and Pade parametrizations. In
general, our research can reveal any potential biases in the CPL
parametrization and determine the consistency of observational data with the
$\Lambda$CDM cosmology or alternative dark energy models. We find that in the
generalizations of CPL parametrization, the deviation from $w_{\Lambda}=-1$ is
more pronounced when we utilize the combinations of DESI BAO, CMB and various
Pantheon+, Union 3, and DES 5YR SNIa compilations.
