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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

(1) Boole, G. Differential Equations, Supplementary Volume, 1865.Google Scholar
(2) Goursat, E., Cours d’Analyse Mathématique, Vol. 11, 5th ed., 1933.Google Scholar
(3) Hill, M.J M., Proc. Lond. Math. Soc., Vol. 17, 1918, p. 149.Google Scholar
(4) Ince, E. L., Ordinary Differential Equations, 1927 Google Scholar
(5) Piaggio, H. T. H., J Lond. Math. Soc., Vol. 13, 1938, p. 264.Google Scholar
(6) de la Vallée Poussin, C. J, Cours d’Analyse Ininitésimale, Vol. 11, 7th ed., 1937 Google Scholar
(7) Srinivasiengar, C. N, Half-yearly J Mysore University, Vol. 5, 1931.Google Scholar
(8) Srinivasiengar, C. N, J Indian Math. Soc., Vol. 20, 1933, p. 157 Google Scholar
(9) Srinivasienagar, C. N, Tôhoku Math J., Vol. 41, 1936, p. 458.Google Scholar
(10) Srinivasienagar, C. N, Ibid., Vol. 42, 1936, p. 284.Google Scholar
(11) Wilson, E. B., Adznnced Calculus, 1911, p. 230.Google Scholar