In many real-world applications, data availability is limited, posing a fundamental challenge to the performance and reliability of machine learning models. While large neural models excel in high-data regimes, their effectiveness diminishes with fewer observations. In contrast, Gaussian Processes (GPs) offer a principled and interpretable approach for small-data scenarios due to their flexibility and strong inductive priors. In this work, we investigate the impact of inductive bias informativeness on the performance of GP models by leveraging Linear Ordinary Differential Equation Gaussian Processes (LODE-GPs), a subclass of GPs constrained by linear ODEs. We propose a suite of increasingly informative ODE-based prior structures, derived from variations of a linearized bipendulum system, to systematically quantify how model performance scales with the strength and correctness of prior knowledge. We evaluate these variants across multiple dataset sizes, noise levels, and inductive priors, comparing their behavior in terms of MAP estimates, training and test MSE, ODE satisfaction, and noise level recovery. Our results reveal that more informative or correct inductive priors lead to improved data efficiency and generalization, especially in low-sample regimes, while incorrect priors can degrade performance significantly. Notably, even partial priors can approximate full-system performance given enough data. These findings underline the importance of tailoring inductive bias to task-specific structure when designing models for data-scarce environments.