Ordinary Differential Equations
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.
KeywordsOrdinary Differential Equation LAPLACE Transform Order Differential Equation Negative Real Part Complex Conjugate Root
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- 1.A thorough treatment of the material in this section maybe found in DOETSCH (1971), Ch. 3.Google Scholar
- 2.A very large number of applications may be found in Thompson (1957), Ch. 3.Google Scholar
- 3.See, for example, Kaplan (1962) and van der Pol & Bremmer (1955), Ch. 8.Google Scholar
- 4.Logarithmic terms appear in the second solution whenever ν is an integer. See Section 20.6.Google Scholar