On closed-form solutions to a class of ordinary differential equations - Badani, Dhrushil (International Journal of Advanced Mathematical Sciences, 2014)
In this paper,closed-form solutions in terms of integral(s) to any second and third order linear non-homogeneous constant-coefficient ordinary differential equations as well as the second order non-homogeneous Cauchy-Euler equation, are derived. The method is generalized for nth order linear non-homogeneous constant-coefficient ordinary differential equations. A similar method is used to derive closed-form solutions to second order linear non-homogeneous non- constant coefficient ordinary differential equations. We then demonstrate an application of the method to recurrence relations of the second order.   Keywords: Closed-form, Ordinary Differential Equations, Recurrence Relations