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Linear Ordinary Differential Equations with Constant Coefficients: Identification of Boole's Integral with that of Cauchy

Published online by Cambridge University Press:  21 January 2009

D. H. Parsons
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We consider an equation with constant coefficients

where a≠0 and f(x) is continuous in a suitable interval. Suppose that the symbolic polynomial P(D) has been fully decomposed into its (real or complex) linear factors, so that the equation may be written

where b1, …, bq are distinct, and m1+…+mq = n. The Complementary Function being now known, we may write down a particular integral of (1) by Cauchy's method.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 43 , December 1960 , pp. 13 - 15
Copyright
Copyright © Edinburgh Mathematical Society 1960