This project demonstrates solving higher-order ODEs using Euler and Runge-Kutta methods in MATLAB. It introduces numerical techniques for approximating solutions where analytical methods fall short. Euler’s method is applied to basic ODEs, while RK-2 and RK-4 offer improved accuracy. A mass-spring-damper system models real-world dynamics and is solved using RK-4. MATLAB scripts allow parameter tuning and visualize damping effects. Graphs show system behavior under different damping conditions. The project highlights the impact of step size and method choice on solution precision. It emphasizes the value of numerical methods in engineering analysis. Overall, this project tries to blend theory, computation, and application in a clear, hands-on approach.