On closed-form solutions to a class of ordinary differential equations
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Abstract
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
References
Andrei Polyanin & Valentin Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Second Edition, Chapman and Hall/CRC, (2002).
William Boyce & Richard Di Prima, Elementary Differential Equations, Eighth Edition, Wiley, (2004).
Daniel Zwillinger, Handbook of Differential Equations, Third Edition, Academic Press, (1997).