Sequences of nonlinear differential equations with related solutions
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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.
KeywordsDifferential Equation Exact Solution Rational Function Applied Mathematic Original Equation
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