Abstract— Inhomogeneous linear ordinary differential equations (ODEs) and systems of ODEs can be solved in a variety ofways. However, hardware circuits that can perform the effificientanalog computation to solve them are rarely in the literature.To address such problems, this paper proposes a general methodof using a memristor-capacitor (M-C) circuit to solve inhomogeneous linear ODEs and systems of ODEs of any order in initialvalue problems. The M-C circuit can match the coeffificients ofthe equations sought by adjusting the memristor resistance valueaccording to the coeffificient formula proposed in the paper, whichhas higher programmability. Then, some ODEs and systemsof ODEs are given in the paper as examples to evaluate theproposed method. According to the comparison results basedon MATLAB software simulation and the simulation based onOrCAD software, the designed M-C circuit has an effectiveimprovement in speed and the accuracy exceeds 99.95% insoftware simulation. Based on practical verifification, this papergives the actual M-C circuit experiment based on PCB. Moreover,the proposed method can be used to quickly solve the objectmotion state in the spring mass damping system in actualengineering, and the accuracy can reach 99.98%.

Index Terms— Memristor, ordinary differential equation,memristive circuit, spring mass damping system.