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Mayer’s Method of Solving the Equation dz = P dx + Q dy

Published online by Cambridge University Press:  03 November 2016

M.L. Cartwright
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Extract

It has been pointed out that Mayer's method of solving the differential equation

is quite general and only requires one integration, whereas the other general methods require two, or even thee, integrations. The reason for this is rather obscure in most text-books ; and the proof of the validity of the method rests on an existence theorem which leads to a solution of an apparently different form. I shall prove here that the two forms are identical.

Type
Research Article
Information
The Mathematical Gazette , Volume 18 , Issue 228 , May 1934 , pp. 105 - 107
Copyright
Copyright © The Mathematical Association 1934

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References

page no 105 note * See Underwood, F., Math. Gazette, XVII (1933), 105–111.Google Scholar

† See Bieberbach, L., Differntialgleichungen, 3rd edition, Berlin (1930). 278–9Google Scholar; Poussin, de la Vallée, Cours d’Analyse Infinitésimale, II, 6th edition, Paris (1928), 299.Google Scholar

‡ See L. Bieberbach, loc. cit., 276–278.

page no 107 note * See Ince, E.L., Ordinary Difjerential Equations (1927), 52–56 Google Scholar; Piaggio, H.T.H., An Elementary Treatise on Differential Equations and their Applications (1931), 110–112 Google Scholar; Goursst, E., Cours d’Analyse mathématique, Paris (1918), Vol. II, 572–574.Google Scholar