코시오일러방정식Cauchy-Euler_equation (rev. 1.3)
다음 형태의 선형 미분방정식을 Cauchy-Euler equation, Euler equation, equidimensional equation이라고 한다.
$\displaystyle a_n x^n \frac{d^ny}{dx^n} + a_{n-1} x^{n-1} \frac{d^{n-1}y}{dx^{n-1}} + \cdots + a_1 x \frac{dy}{dx}+a_0y=g(x)$
homogeneous second-order equation:$\displaystyle ax^2\frac{d^2y}{dx^2}+bx\frac{dy}{dx}+cy=0$
i.e.$\displaystyle ax^2y{' '}+bxy'+cy=0$