This study aims to analyze a damped Mathieu-cubic quintic Duffing oscillator, a parametric nonlinear oscillatory dynamical system with applications in optics, quantum physics, and general relativity. The non-perturbative approach (NPA) is employed to transform the nonlinear ordinary differential equation into a linear equation, providing an approximate solution without relying on traditional perturbation methods. The method is extended to determine optimal solutions for large amplitude fluctuations and validate the derived parametric equation against the original equation. Stability analysis is conducted using Floquet theory, and transition curves are examined. The NPA is characterized by its clear principles, practicality, and high numerical precision, making it suitable for addressing nonlinear parametric problems. The study includes a detailed analysis of the damped Mathieu cubic–quintic Duffing oscillator, including special cases, enhanced solutions, and the presence of damping terms. The results demonstrate the effectiveness of the NPA in analyzing the frequency-amplitude relationship and stability behavior of the system.This study aims to analyze a damped Mathieu-cubic quintic Duffing oscillator, a parametric nonlinear oscillatory dynamical system with applications in optics, quantum physics, and general relativity. The non-perturbative approach (NPA) is employed to transform the nonlinear ordinary differential equation into a linear equation, providing an approximate solution without relying on traditional perturbation methods. The method is extended to determine optimal solutions for large amplitude fluctuations and validate the derived parametric equation against the original equation. Stability analysis is conducted using Floquet theory, and transition curves are examined. The NPA is characterized by its clear principles, practicality, and high numerical precision, making it suitable for addressing nonlinear parametric problems. The study includes a detailed analysis of the damped Mathieu cubic–quintic Duffing oscillator, including special cases, enhanced solutions, and the presence of damping terms. The results demonstrate the effectiveness of the NPA in analyzing the frequency-amplitude relationship and stability behavior of the system.