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Solution of Differential Equations by Operational Methods

Published online by Cambridge University Press:  03 November 2016

Extract

The method of solving linear differential equations with constant coefficients by using the operator D, which is given in elementary textbooks, was introduced in 1841 by Boole. In spite of the developments summarised below it remains the best method available for certain types of problem. As usually presented it is a tentative process, justified only by substitution in the original equation of the result produced. It is used only to obtain particular integrals, although it can be adapted to deal with complementary functions. This is not done in practice, however, since these can usually be written down directly.

Type
Operational Methods
Copyright
Copyright © Mathematical Association 1947

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References

page note 148 † These expressions should include the expression {1/R(D)} 0, or similar complementary function terms, for completeness. As stated above they are usually omitted.

page note 149 † See previous footnote.