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4. On the Linear Differential Equation of the Second Order

Published online by Cambridge University Press:  15 September 2014

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Extract

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.

A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

Type
Proceedings 1875-76
Copyright
Copyright © Royal Society of Edinburgh 1878

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