The present tutorial proposes to use concepts of physics and mathematics to help behavioral scientists to use differential equations in their studies. It focuses on the first-order and the second-order (damped oscillator) differential equation. Simple examples allow to detail the meaning of the coefficients, the conditions of applicability of these differential equations, the underlying hypothesis, and their consequences for the researcher willing to use them. More complex psychological examples demonstrate the importance of parameters' interpretation. Particular attention is paid to how potential external perturbations should be considered. (PsycInfo Database Record (c) 2022 APA, all rights reserved).