Discovering Differential Equations from Data: A Didactic Approach with Regression Analysis

Differential equations are used to predict a wide range of phenomena in physics, engineering, and other fields. In education, differential equations are usually introduced axiomatically, and experimental results are predicted from them. However, in practice, there is often a different procedure. First of all the mesurement data is available and in a second step it is desired to find the differential equation on which it is based. In this paper, a didactic approach is proposed to determine the underlying differential equation from a given dataset. To achieve this, the concept of regression is used, and the method is demonstrated through a practical example.