SOLUTION OF BESSEL’S DIFFERENTIAL EQUATION BY LAPLACE UTION OF BESSEL’S DIFFERENTIAL EQUATION BY LAPLACE TRANSFORM METHOD UTION OF BESSEL’S DIFFERENTIAL EQUATION BY LAPLACE

Abstract

Bessel’s equation is the whole family of differential equation, specially ordinary differential equation and frequently occur in various fields of science, applied mathematics and mathematical physics involving cylindrical symmetry. In this thesis, we proposed a most general form of linear second order ordinary differential equation of variable coefficient in the form of Bessel’s kind. We convert the proposed Bessel’s differential equation into an algebraic equation for transformed function by using Laplace transform. Solving this second order ordinary differential equation of variable coefficient, using reduction of order and power series method of solving differential equation and applying inverse Laplace transform general 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 softwares like mathematica and computer programming (c++).