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The Incompleteness of “Complete” Primitives of Differential Equations

Published online by Cambridge University Press:  03 November 2016

H. T H. Piaggio
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Extract

Dr. C. N Srinivasiengar, in his published papers (7, 8, 9 and 10), and Dr. W E. Deming, in a private letter, gave examples of differential equations for which the so-called complete primitives are not really complete, and yet the supplementary solutions are not singular solutions in the envelope sense. In the ensuing correspondence I expanded a remark of E. B. Wilson (11) “It may happen that the arbitrary constant C enters into the expression F(x, y, C) = 0 in such a way that when C becomes positively infinite (or negatively infinite) the curve F(x, y, C) = 0 approaches a definite limiting position which is a solution of the differential equation, such solutions are called infinite solutions.”

Type
Research Article
Information
The Mathematical Gazette , Volume 23 , Issue 253 , February 1939 , pp. 49 - 57
Copyright
Copyright © Mathematical Association 1939 

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References

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(6) de la Vallée Poussin, C. J, Cours d’Analyse Ininitésimale, Vol. 11, 7th ed., 1937 Google Scholar
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