<p>The second-order differential equation for the non-linear radial oscillations of a transversely-isotropic hyperelastic tube has been postulated and derived based on certain requirements for the strain-energy function and the applied pressure. Lie point symmetry analysis has been used for the non-linear radial oscillatory system composed of neo-Hookean material to address the challenges in solving this equation. A comparison is conducted between the differential equations before and after the Lie transformation. Using Lie point symmetries, we demonstrate that the non-linear differential equations of the transversely-isotropic hyperelastic tube enhance non-periodic oscillations, which can contribute to the prediction of material reliability. This article aims to provide a comprehensive introduction and an application overview in the field of dynamical systems.</p>