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Miscellany

On the well-definedness of the order of an ordinary differential equation

Pages 358-362 | Received 11 Jan 2005, Published online: 20 Feb 2007
 

Abstract

It is proved that if the differential equations y ( n )=f(x, y, y′, …, y ( n −1 )) and y ( m )=g(x, y, y′, …, y ( n −1 )) have the same particular solutions in a suitable region where f and g are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical Lipschitz condition), then n = m and the functions f and g are equal. This note could find classroom use in a course on differential equations as enrichment material for the unit on the existence and uniqueness theorems for solutions of initial value problems.

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