Bessel's Equation is a second-order linear differential equation that arises in various physical problems, particularly in cylindrical coordinates. It is commonly expressed in the form x^2 y'' + x y' + (x^2 - n^2) y = 0 , where n is a constant. The solutions to this equation are known as Bessel functions, which are important in fields such as acoustics, electromagnetism, and heat conduction. Bessel functions come in two main types: Bessel functions of the first kind and Bessel functions of the second kind. These functions are used to describe waveforms and oscillations in cylindrical systems, such as vibrations of a circular drum or the propagation of waves in a cylindrical pipe. Understanding Bessel's Equation and its solutions is crucial for solving many engineering and physics problems.