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 ( .
