Overtaking on a dual-lane road with the presence of oncoming vehicles poses a considerable challenge in the field of autonomous driving. With the assistance of high-definition maps, autonomous vehicles can plan a relatively safe trajectory for executing overtaking maneuvers. However, the creation of high-definition maps requires extensive preparation, and in rural areas where dual two-lane roads are common, there is little pre-mapping to provide high-definition maps. This paper proposes an end-to-end model called OG-Net (Overtaking Guide Net), which accomplishes overtaking tasks without map generation or communication with other vehicles. OG-Net initially evaluates the likelihood of a successful overtaking maneuver before executing the necessary actions. It incorporates the derived probability value with a set of simple parameters and utilizes a Gaussian differential controller to determine the subsequent vehicle movements. The Gaussian differential controller effectively adapts a fixed geometric curve to various driving scenarios. Unlike conventional autonomous driving models, this approach employs uncomplicated parameters rather than RNN-series networks to integrate contextual information for overtaking guidance. Furthermore, this research curated a new end-to-end overtaking dataset, CarlaLanePass, comprising first-view image sequences, overtaking success rates, and real-time vehicle status during the overtaking process. Extensive experiments conducted on diverse road scenes using the Carla platform support the validity of our model in achieving successful overtaking maneuvers.