SOME ASPECTS OF LEGENDRE AND CHEBYSHEV DIFFERENTIAL EQUATION

Abstract

Legendre and Chebyshev equations are the whole family of differential equation,Specialy ordinary differential equation and frequently occurrs in various fields of science and mathematics ,physics involving spherical symmetry.In this thesis , we proposed a most genral form of linear second ordre ordinary differential equation of variable coefficient in the form of Legendre and Chebyshev kind .Solving this second ordre ordinary differential equation of variable coefficient using power seres method and Laplace transform method genral solution of the problem is obtained. Graphical solution and numerical values are presented to show the performance and accuracy of the proposed method. To obtain numerical value and graphical solution we used some soft ware like mathematica and computer programming ( .