Cauchy–Euler equation

Typical solution curves for a second-order Euler–Cauchy equation for the case of two real roots

Typical solution curves for a second-order Euler–Cauchy equation for the case of a double root

Typical solution curves for a second-order Euler–Cauchy equation for the case of complex roots

In mathematics, a Cauchy–Euler equation (also known as the Euler–Cauchy equation, or simply Euler's equation) is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of the particularly simple equidimensional structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly.

单词	Euler differential equation
释义	Euler differential equation 英语百科 Cauchy–Euler equation In mathematics, a Cauchy–Euler equation (also known as the Euler–Cauchy equation, or simply Euler's equation) is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of the particularly simple equidimensional structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly.
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Euler differential equation

Cauchy–Euler equation