Definition:Cauchy-Euler Equation/General Form

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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.

Source of Name

This entry was named for Augustin Louis Cauchy and Leonhard Paul Euler.