This study uses machine learning to predict the convergence results of the Duffing equation with and without damping. The Duffing equation represents a nonlinear second-order differential equation with interesting behavior in undamped free vibration and forced vibration with damping. Convergence alternates randomly between 1 and -1 in undamped free vibration, depending on initial conditions. For forced vibration with damping, multiple factors influence vibration patterns. We utilize the fourth-order Runge-Kutta method to collect convergence results for both conditions. Machine learning techniques, specifically the long short term memory (LSTM) and LSTM-Neural Network (LSTM-NN) method, are employed to predict these convergence values. The LSTM-NN model is a hybrid approach that combines the LSTM method with the addition of hidden layers of neurons. Both the LSTM and LSTM-NN models are thoroughly explored and analyzed in this research. The research process involves three stages: data preprocessing, training, and verification. The results show that the LSTM-NN model becomes more adept at predicting binary datasets, boasting an impressive accuracy of up to 98%. However, when it comes to predicting multiple solutions, the traditional LSTM method outperforms the LSTM-NN approach.