Titlebook: Introduction to the Theory and Application of the Laplace Transformation; Gustav Doetsch Book 1974 Springer-Verlag Berlin Heidelberg 1974

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The Initial Value Problem of Ordinary Differential Equations with Constant Coefficients,ntegrating ordinary linear differential equations with constant coefficients in the interval . ≧ 0, for specified values of the solution and some of its derivatives at . = 0, the initial values (Initial Value Problem). This is a problem which may be solved by a familiar classical technique: First on

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The Ordinary Differential Equation, specifying Initial Values for Derivatives of Arbitrary Order, a 0. However, one could encounter some initial value problem with . specified values at . = 0 for derivatives of arbitrary order. For instance, for same third order differential equation one might specify the initial values . .(0), . .(0), . . (0). In this case, we would solve the problem as if . (0)

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The Ordinary Linear Differential Equation in the Space of Distributions,ibution-derivative equations.” In the latter, the given and the sought quantities are distributions. To emphasize the analogy to the case of functions, we shall employ here for the designation of distributions lower case letters like ., ., . . . (which are usually reserved for functions) instead of

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