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Stationary solutions of certain nonlinear differential equations

Authors
Journal
Journal of the Franklin Institute
0016-0032
Publisher
Elsevier
Publication Date
Volume
254
Issue
1
Identifiers
DOI: 10.1016/0016-0032(52)90003-3
Disciplines
  • Mathematics

Abstract

Abstract The differential equation x ̈ + b dot x + x + (a − cx 2)x cos2t + ex 3 = 0 , encountered in applications, is investigated by the perturbation theory. Equations of the first approximation are discussed in the general case as well as in a number of particular cases. In Part II the problem of the maintenance of the oscillation of a pendulum by alternating current is studied and it is shown that it is expressible in terms of this differential equation.

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