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++).
