\begin{definition}[Definition:Cauchy-Euler Equation/General Form]
Let $n \in \Z_{>0}$ be a strictly positive integer.
The linear ordinary differential equation:
:$a_n x^n \, \map {y^{\paren n} } x + \dotsb + a_1 x \, \map {y'} x + a_0 \, \map y x = 0$
is the '''$n$th order Cauchy-Euler equation'''.
{{NamedforDef|Augustin Louis Cauchy|name2 = Leonhard Paul Euler}}
Category:Definitions/Ordinary Differential Equations
\end{definition}