Application of operator factorization in linear differential equation

This paper presents the use of operator factorization in solving linear differential equations. First, we consider an nth order linear differential equation with constant coefficients. The general solution is obtained using the method of operator factorization regardless of the nature of the roots of the characteristic polynomial. Secondly, the same method is applied in solving the Euler equations. By a change of variable the equation is reduced to a linear differential equation with constant coefficients. Finally, the method is modified for the case of second order linear differential equations with variable coefficients. The paper shows how a single solution of the homogeneous equation can be used to find the general solution of the non-homogeneous equation using operator factorization