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On the general solution of a linear second order equation with variable coefficients

Published online by Cambridge University Press:  26 February 2010

David L. Clements
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Box 498 G.P.O., Adelaide SA 5001, Australia.
C. Rogers
Affiliation:
Department of Applied Mathematics, The University of Waterloo, Canada.
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Abstract

A linear second order partial differential equation with variable coefficients is considered. The equation is relevant in a number of physical situations. Simple general solutions are obtained subject to the coefficients satisfying certain constraints.

Type
Research Article
Copyright
Copyright © University College London 1983

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References

Eason, G.. Wave propagation in inhomogeneous elastic media. Bull. Seism. Soc. Amer., 57 (1967), 1267- 1277.Google Scholar
Thomson, L. M. Milne. Antiplane elastic systems (Springer-Verlag, 1960).Google Scholar
Synge, J. L.. On the vibrations of a heterogeneous string. Quart. Appl. Math., 39 (1981), 292297.Google Scholar
Teipel, I.. Nichtlineare Wellenausbreitungsvoryange in elastischen Leitungen. Ada Mech., 16 (1973), 93106.Google Scholar
Webster, A. G.. Acoustical impedance and the theory of horns and of the phonograph. Proc. Nat. Acad. Sci., 5 (1919), 275282.CrossRefGoogle ScholarPubMed