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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. This characteristic equation is a nonlinear eigenproblem and there are many methods to compute the spectrum numerically. In some special situations it is possible to solve the characteristic equation explicitly.