Definition:Cauchy-Euler Equation

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The linear second order ordinary differential equation:

$x^2 \dfrac {\d^2 y} {\d x^2} + p x \dfrac {\d y} {\d x} + q y = 0$

is the 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.

Also known as

The Cauchy-Euler equation is also known as:

  • Euler's equation
  • The Euler-Cauchy equation
  • Euler's (or Cauchy's) equidimensional equation.

Also see

Source of Name

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