Bessels Differential Equation And The Aging Spring Problem

In this paper we study the aging spring equation without dampingrnX= (t) + e−at+b x(t)=0 ,rnor the most general one with dampingrn(t) + dx= (t) + e−at x(t)=0rnwhich is a special cases of homogeneous linear second order ODE with variable coefficients.rnWe will show that, with a suitable change of variables, this equation of aging spring problemrncan be transformed into Bessel differential equation and hence the solution can be expressedrnin terms of Bessel functions

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