Solving Some Types of the Second and Third Order Spectral Linear Ordinary Differential Equations

Abstract

     Our article is for finding complete primitive for two different kinds of linear ordinary differential equations in a spectral type. First kind is consisting of two different types of coefficients of order two; one of them is polynomials, where as the other type is continuous functions and both are of real types. The second kind is for a third order, and here the coefficients of this kind are also several real polynomials, and in both kinds of spectral linear ordinary differential equations, the coefficients are converted to the constants via varying the independent variable to a new one.  We gave examples to explain our mechanism.