Significant advancements have been made in hyperspectral image (HSI) super-resolution with the development of deep-learning techniques. However, the current application of deep neural network architectures to HSI super-resolution heavily relies on empirical design strategies, which can potentially impede the improvement of image reconstruction performance and introduce distortions in the results. To address this, we propose an innovative HSI super-resolution network called dual ordinary differential equations (Dual ODEs). Drawing inspiration from ordinary differential equations (ODEs), our approach offers reliable guidelines for the design of HSI super-resolution networks. The Dual ODE model leverages a spatial ODE block to extract spatial information and a spectral ODE block to capture internal spectral features. This is accomplished by redefining the conventional residual module using the multiple ODE functions method. To evaluate the performance of our model, we conducted extensive experiments on four benchmark HSI datasets. The results conclusively demonstrate the superiority of our Dual ODE approach over state-of-the-art models. Moreover, our approach incorporates a small number of parameters while maintaining an interpretable model design, thereby reducing model complexity.