Accurate segmentation of cardiac anatomy in echocardiography is essential for cardiovascular diagnosis and treatment. Yet echocardiography is prone to deformation and speckle noise, causing frame-to-frame segmentation jitter. Even with high accuracy in single-frame segmentation, temporal instability can weaken functional estimates and impair clinical interpretability. To address these issues, we propose DyL-UNet, a dynamic learning-based temporal consistency U-Net segmentation architecture designed to achieve temporally stable and precise echocardiographic segmentation. The framework constructs an Echo-Dynamics Graph (EDG) through dynamic learning to extract dynamic information from videos. DyL-UNet incorporates multiple Swin-Transformer-based encoder-decoder branches for processing single-frame images. It further introduces Cardiac Phase-Dynamics Attention (CPDA) at the skip connections, which uses EDG-encoded dynamic features and cardiac-phase cues to enforce temporal consistency during segmentation. Extensive experiments on the CAMUS and EchoNet-Dynamic datasets demonstrate that DyL-UNet maintains segmentation accuracy comparable to existing methods while achieving superior temporal consistency, providing a reliable solution for automated clinical echocardiography.