다음 형태의 선형 미분방정식을 '''Cauchy-Euler equation, Euler equation, equidimensional equation'''이라고 한다.
 $a_n x^n \frac{d^ny}{dx^n} + a_{n-1} x^{n-1} \frac{d^{n-1}y}{dx^{n-1}} + \cdots + a_1 x \frac{dy}{dx}+a_0y=g(x)$

homogeneous second-order equation:
 $ax^2\frac{d^2y}{dx^2}+bx\frac{dy}{dx}+cy=0$
i.e.
 $ax^2y{' '}+bxy{' '}+cy=0$


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Up: [[미분방정식,differential_equation]]