Ordinary Differential Equations

  • B. Davies
Part of the Applied Mathematical Sciences book series (AMS, volume 25)


Linear differential equations with constant coefficients are an important area of application of the Laplace transform. As a prelude to the discussion of such problems we discuss first two particularly simple examples, since the connection with the classical methods of solution is readily apparent in these cases.


Ordinary Differential Equation Asymptotic Form LAPLACE Transform Order Differential Equation Negative Real Part 
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  1. 2.
    A very large number of applications may be found in THOMPSON (1957), Ch. 3.Google Scholar
  2. 3.
    See, for example, KAPLAN (1962) and VAN DER POL $ BREMMER (1955), Ch. 8.Google Scholar
  3. 4.
    Logarithmic terms appear in the second solution whenever y is an integer. See Section 20.6.Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • B. Davies
    • 1
  1. 1.The Australian National UniversityCanberraAustralia

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