Although high-performance deep neural networks are in high demand in edge environments, computation resources are strictly limited in edge devices, and light-weight neural network techniques, such as Depthwise Separable Convolution (DSC), have been developed. ResNet is one of conventional deep neural network models that stack a lot of layers and parameters for a higher accuracy. To reduce the parameter size of ResNet, by utilizing a similarity to ODE (Ordinary Differential Equation), Neural ODE repeatedly uses most of weight parameters instead of having a lot of different parameters. Thus, Neural ODE becomes significantly small compared to that of ResNet so that it can be implemented in resource-limited edge devices. In this paper, a combination of Neural ODE and DSC, called dsODENet, is designed and implemented for FPGAs (Field-Programmable Gate Arrays). dsODENet is then applied to edge domain adaptation as a practical use case and evaluated with image classification datasets. It is implemented on Xilinx ZCU104 board and evaluated in terms of domain adaptation accuracy, training speed, FPGA resource utilization, and speedup rate compared to a software execution. The results demonstrate that dsODENet is comparable to or slightly better than our baseline Neural ODE implementation in terms of domain adaptation accuracy, while the total parameter size without pre- and post-processing layers is reduced by 54.2% to 79.8%. The FPGA implementation accelerates the prediction tasks by 27.9 times faster than a software implementation.