Frobenius Solution

Abstract

For A(x) $\ne 0$, the normalized form of differential equation

$$\begin{aligned} A(x)\,y''(x)+B(x)\,y'(x)+C(x)\, y(x)~=~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$

is

$$\begin{aligned} y''(x)+M(x)\,y'(x)+N(x)\, y(x)~=~0~~,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$

where

$$\begin{aligned} M(x)~=~\frac{B(x)}{A(x)}~~;~~N(x)~=~\frac{C(x)}{A(x)}~~.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$

.