> [!NOTE] Definition (Ordinary Differential Equation) > An *ordinary differential equation* is [[Differential Equation|differential equation]] involving exactly one independent variable. # Properties **Classification**: A [[Scalar Ordinary Differential Equation|scalar]] ODE is one that involves exactly one dependent variable. An ODE is [[Linear Differential Equation|linear]] iff all the dependent variables and their derivatives appear to the first power. An ODE is [[Autonomous Ordinary Differential Equation|autonomous]] if the independent variable only features as an argument of a dependent variable. An ODE is [[Homogeneous Ordinary Differential Equation|homogeneous]] iff there is no term that doesn't involve a dependent variable or any of their derivatives. **Solution**: an ODE that involves more than one dependent variable is not determined. [[System of Differential Equations]] is determined if number of equation is the same as number of dependent variables and no two equations are equivalent. An application, [[Reduction of Order of Scalar Ordinary Differential Equations]] asserts that [[System of First Order Ordinary Differential Equations]]; [[2 x 2 System of First Order Ordinary Differential Equations]]; # Applications **Modelling reaction kinetics**: [[Law of Mass Action]].