Inequalities for solutions of linear differential equations a contribution to the theory of servomechanisms

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Abstract
Consider the nth order differential equation where the coefficients cv are real constants and f is a real function continuous in the interval a≦ x ≦ b. The following theorem will be proved in §4:If the characteristic equation of (I) has no purely imaginary roots, then a particular integral η (x) can always be found which satisfies the inequality where C is a certain function of the cv only and M is the maximum of |f|. In particular we may take C = 1 if all roots of the characteristic equation are real.