An approximation to solutions of linear ODE by cubic interpolation

We present a method of integration for non-autonomous non-homogeneous systems of linear ordinary differential equation (ODE), which is based in both, the cubic polynomial segmentary interpolation and the minimal square method. This method is valid for nonhomogeneous ordinary linear second order differential equations in the neighborhood of regular and singular regular points. We illustrate the method with the Mathieu and Bessel equations and two other equations that arise in the study of quantum systems with axial symmetry, which are versions of the spheroidal wave equation.