\begin{definition}[Definition:First Order Ordinary Differential Equation]
A '''first order ordinary differential equation''' is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $1$.
The general '''first order ODE''' can be written as:
:$\map F {x, y, \dfrac {\d y} {\d x} }$
or, using prime notation:
:$\map F {x, y, y'}$
If it is possible to do so, then it is often convenient to present such an equation in the form:
:$\dfrac {\d y} {\d x} = \map f {x, y}$
that is:
:$y' = \map f {x, y}$
It can also be seen presented in the form:
:$\map \phi {x, y, y'} = 0$
\end{definition}