In this communication we have used Bickley’s method for the construction of a sixth order spline function and apply it to solve the linear fifth order differential equations of the form yx(x)+g (x)y(x)= r(x) where g(x) and r(x) are given functions with the two different problems of different boundary conditions. The method is illustrated by applying it to solve some problems to demonstrate the application of the methods discussed.
 E. A. Boquez and J. D. A. Walker, “Fourth Order Finite Difference Methods for Two Point Boundary Value Problems,” IMA Journal of Numerical Analysis, Vol. 4, No. 1, 1984. pp. 69-82. doi:10.1093/imanum/4.1.69
 M. M. A. Chawla, “Fourth Order Tridiagonal Finite Difference Method for General Two Point Boundary Value Problems with Mixed Boundary Conditions,” Journal of the Institute of Mathematics and Its Applications, Vol. 21, No. 1, 1978, pp. 83-93. doi:10.1093/imamat/21.1.83
 P. S. Rama Chandra Rao, “Special Multistep Methods Based on Numerical Differentiation for Solving the Initial Value Problem,” Applied Mathematics and Computation, Vol. 181, No. 1, 2006, pp. 500-510. doi:10.1016/j.amc.2005.12.063