As the demand for scientific and engineering computing continues to soar, ordinary differential equations (ODEs) have gained paramount significance across diverse domains, including physics, climate modeling, and artificial intelligence. Nevertheless, traditional hardware based on the von Neumann architecture encounters bottlenecks in terms of speed and energy efficiency when tackling ODEs. To overcome these limitations, researchers are actively exploring novel hardware alternatives, with memristors emerging as a frontrunner due to their exceptional energy efficiency and parallel processing prowess. Despite the notable advancements in memristor-based partial differential equation solvers, directly adapting them for ODE solving remains a formidable challenge. To ensure precision, a substantial number of devices must undergo reprogramming, or significant computational resources must be expended, thereby escalating system complexity and constraining practical applications. Hence, the development of efficient and accurate ODE solvers has become of utmost importance.