Ordinary differential equations are mathematical equations that describe how a system changes over time, based on its current state and the forces acting upon it. Synonyms for this term include ODEs, differential equations, and differential equations of one variable. These equations are used in a wide range of scientific and engineering applications, from modeling chemical reactions to analyzing the behavior of celestial bodies. ODEs are widely studied and have led to many important solutions and discoveries in mathematics and science. Other related terms include partial differential equations, difference equations, and stochastic differential equations.