Remaining Useful Life (RUL) prediction contributes to ensuring the reliability of mechanical systems and improving their maintenance plans. Recently, prediction methods based on deep learning have undergone rapid development. However, there are significant differences between multivariate monitoring sequences and utilizing a single model for feature extraction, which leads to reaching suboptimization. Additionally, focusing solely on a specific feature dimension usually imposes notable limitations on the model. This paper proposes a Closed-form Continuous-depth neural (CfC)-based hybrid difference Features Re-representation Network (CfC-F2RN) for RUL prediction. This method comprehensively utilizes hybrid difference features through two stages: initial feature representation and feature re-representation. In the initial feature representation stage, a Long Short-Term Memory (LSTM) is employed to capture the hidden state information of each time step in sequence data. Next, a novel attention mechanism is utilized to extract the hidden states and obtain a deep feature map. In the feature re-representation stage, the encoded features are re-represented using a decoder composed of the CfC model. Finally, the hidden state of the last LSTM unit in the encoder, serving as supplementary information, is combined with the decoded features to form a dual-latent feature representation of the mixed differential features. The prediction subnetwork is then adopted to accomplish RUL prediction. The superiority of CfC-F2RN is substantiated through benchmarking against established methods using the C-MAPSS dataset.