\begin{definition}[Definition:Linear First Order Ordinary Differential Equation]
A '''linear first order ordinary differential equation''' is a differential equation which is in (or can be manipulated into) the form:
:$\dfrac {\d y} {\d x} + \map P x y = \map Q x$
where $\map P x$ and $\map Q x$ are functions of $x$.
It is:
:Linear because both $\dfrac {\d y} {\d x}$ and $y$ appear to the first power, and do not occur multiplied together
:First order because the highest derivative is $\dfrac {\d y} {\d x}$
:Ordinary because there are no partial derivatives occurring in it.
\end{definition}