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Annali di Matematica Pura ed Applicata

, Volume 81, Issue 1, pp 249–258 | Cite as

Sequences of nonlinear differential equations with related solutions

  • Mostafa A. Abdelkader
Article

Summary

A second-order nonlinear differential equation which occurs (together with variants of it) in many problems of applied mathematics, physics and engineering is here reduced to a first-order equation. This equation contains a parameter which is a quadratic rational function of two parameters appearing in the original equation. By applying a certain identity for a quadratic rational function, two (finite or infinite) sequences of nonlinear differential equations are generated whose solutions are determinable whenever the solution of any equation belonging to a sequence is known. The cases amenable to exact solution by quadrature are given.

Keywords

Differential Equation Exact Solution Rational Function Applied Mathematic Original Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Nicola Zanichelli Editore 1969

Authors and Affiliations

  • Mostafa A. Abdelkader

There are no affiliations available

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