Differential equations MOC

Cauchy-Euler differential equations

A Cauchy-Euler ODE or equidimensional ODE is a linear ODE in which each term has equal dimension of the independent variable.

Second order

In the second-order, they have the standard form

Solutions are found by finding the roots of the quadratic

and then

1. If in general,

2. In the case and this may be rewritten as

3. If is a repeated root

Practice problems

• Libretext: §2.5 Cauchy-Euler equations (worked examples)
• 2017. Elementary differential equations and boundary value problems, p. 133 (§3.4 problems 31–34)

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