Ordinary Differential Equation

differential-equations

Definition

Definition

Ordinary differential equation (ODEs) describe the relationships between a function, its derivatives, and a single independent variable. These equations model how a dependent variable’s rate of change is connected to the variable itself.

An $n$-th order ODE is typically represented as

$$F(x,y,y^{\prime },y^{\prime \prime },\dots ,y^{(n)})=0$$

where $y$ is the dependent variable, $x$ is the independent variable, and $F$ is the function of $x$ and $y$, and its derivatives up to the $n$-th order.