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Solutions of a certain partial differential equation

Bateman, H. (1931) Solutions of a certain partial differential equation. Proceedings of the National Academy of Sciences of the United States of America, 17 (10). pp. 562-567. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:BATpnas31a

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Abstract

The partial differential equation ∂u/∂t = x(∂^2u/∂x^2 – u) is readily seen to possess the two particular solutions U1 = xe^(-x tanh t) sech^2t, U2 = e^(-x coth t).


Item Type:Article
Additional Information:© 1931 by the National Academy of Sciences. Communicated September 14, 1931.
Record Number:CaltechAUTHORS:BATpnas31a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BATpnas31a
Alternative URL:http://www.pnas.org/cgi/reprint/17/10/562
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9325
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Dec 2007
Last Modified:26 Dec 2012 09:47

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