\begin{definition}[Definition:Linear nth Order ODE with Constant Coefficients]
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
A '''linear $n$th order ODE with constant coefficient''' is an ordinary differential equation of order $n$ which can be manipulated into the form:
:$\ds \sum_{k \mathop = 0}^n a_k \dfrac {\d^k y} {d x^k} = \map R x$
where $a_k$ is a real constant for all $0 \le k \le n$.
That is:
:$a_n \dfrac {\d^n y} {d x^n} + a_{n - 1} \dfrac {\d^{n - 1} y} {d x^{n - 1} } + \dotsb + a_1 \dfrac {\d y} {d x} + a_0 y = \map R x$
\end{definition}