In this paper, we propose a hardware ordinary differential equation (ODE) solver based on the open-source RISC-V instruction set architecture. Specifically, we target the Lotka-Volterra system of equations and build reconfigurable co- processors implementing the Euler and Runge-Kutta numerical methods of solving ODEs. We develop a range of co-processor configurations with varying degrees of parallelism and resource utilization, as well as a set of domain-specific customized instructions. In addition to simulating our designs, we also deploy them on re-configurable hardware and perform power estimations. The performance of our co-processor is compared with the performance of the numerical methods running on a 64-bit single- core general purpose microprocessor. We establish that, in the best case, our co-processor attains 4.8x performance, at the cost of merely 13.3% more hardware resources and 8.1% additional power dissipation.