# Euler cauchy differential equation

The Cauchy-Euler equation is important in the theory of linear di er-ential equations because it has direct application to Fourier’s method in the study of partial di erential equations. In particular

## Cauchy–Euler equation

The second‐order homogeneous Cauchy‐Euler equidimensional equation has the form. where a, b, and c are constants (and a ≠ 0). The quickest way to solve this linear equation is to is to substitute y = x m and solve for m. If y = x m , then. so
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## The Euler-Cauchy differential equation

A second-order differential equation is called anEuler equation if it can be written as αx2y′′ + βxy′ + γy = 0 where α, β and γ are constants (in fact, we will assume they are real-valued constants).

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## Formulas, Examples on Cauchy-Euler Equation

A more general form of an Euler Equation is, $a{\left( {x - {x_0}} \right)^2}y'' + b\left( {x - {x_0}} \right)y' + cy = 0$ and we can ask for solutions in any interval not containing

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