Abstract
For A(x) \(\ne 0\), the normalized form of differential equation is where .
$$\begin{aligned} A(x)\,y''(x)+B(x)\,y'(x)+C(x)\, y(x)~=~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$
$$\begin{aligned} y''(x)+M(x)\,y'(x)+N(x)\, y(x)~=~0~~,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$
$$\begin{aligned} M(x)~=~\frac{B(x)}{A(x)}~~;~~N(x)~=~\frac{C(x)}{A(x)}~~.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \end{aligned}$$
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