This study investigates the resolution of higher-order linear equations with constant coefficients through the utilization of formulas derived from higher-order differential equations. The primary emphasis lies in the resolution of a particular fourth-order equation. The paper commences by providing an introductory overview of higher-order equations encompassing a comprehensive examination of the existence and uniqueness theorem, the general solution, and the superposition principle as applied to linear equations. It highlights the significance of the Wronskian determinant in this context. The analysis of the proposed solution for the fourth-order equation is conducted resulting in the determination that it does not constitute the general solution. Subsequently, supplementary solutions are presented leading to nonzero Wronskian and confirming the provided solution as the general solution. Furthermore, an additional set of two problems pertaining to higher-order linear differential equations is presented in order to offer additional perspectives and opportunities for problem-solving. The paper concludes by providing a summary of the findings drawing attention to the limitations of the proposed solution and emphasizing the necessity of considering alternative approaches in the context of higher-order linear differential equations.