Cauchy's Homogeneous Linear Equation

Cauchy's Homogeneous Linear Equation:

Consider Homogeneous Linear differential equation as:

(Here a's are constant and X be function of X) is called Cauchy's homogenous linear equation.

is the homogeneous linear equation with variable coefficients. It is also known as Euler's Equation. Equation 1 can be transformed into a linear equation of constant coefficients by the transformation.