Abdi Tadesse (PhD)Belayneh Tilahun2018-07-192023-11-042018-07-192023-11-042014-08http://etd.aau.edu.et/handle/123456789/9330In this paper we study the aging spring equation without damping X= (t) + e−at+b x(t)=0 , or the most general one with damping (t) + dx= (t) + e−at x(t)=0 which is a special cases of homogeneous linear second order ODE with variable coefficients. We will show that, with a suitable change of variables, this equation of aging spring problem can be transformed into Bessel differential equation and hence the solution can be expressed in terms of Bessel functionsenBessel’s Differential EquationAnd the Aging Spring ProblemThesis