The exact solution of system for the special differential equation with the operators

The exact solution of system for the special differential equation with the operators

In this paper, we use the special transformation in general differential equation and obtain the special polynomial. In that case we investigate the potential and super-potential in differential equation. And then we factorized the corresponding equation which give use the first order operators. Finally we will try to calculate the eigen value and exact solution for such system. As we know the special functions play important role in mathematics, physics, chemistry and engineering. Special functions come historically from the study of Sturm- Liouvile problems and eigenvalue problems which are important because under homogeneous boundary conditions imply particular solutions in the form of orthogonal functions. On the other hand the study of exactly, quasi exactly and conditionally solvable potentials is achieved by means of the supersymmetry quantum mechanics which is equivalent to the application of the standard Darboux transform. In this paper we consider the general form of equation and choose the special transformation and modify the corresponding equation.