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THE SOLUTION STABILITY OF VAN DER POL'S EQUATION .
THE SOLUTION STABILITY OF
VAN DER POL'S EQUATION .
by CO. H . TRAN .
HUI - NCU HCMC
Vietnam coth123@math.com & cohtran@math.com Copyright 2004 November 06 2004 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ** Abstract : The Van der Pol differential quation is solved by averaging method . ** Subjects: Vibration Mechanics , The Differential equations . ------------------------------------------------------------------------------------------------------------------------------------------------------------------------Introduction This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation . All rights reserved. Copying or transmitting of this material without the permission of the authors is not allowed . We consider the Van Der Pol differential equation :
[0] Two topics that we will be in discussion are - Finding the steady state solution of this equation by averaging method .- Estimating the stability of solution obtained . 1 .Define the model of problem : We examine the effect of non-linear system under external force caused by the AC generator ( see fig 1. )
( fig 1. ) The differential equation of this model is given in the form 
+ 
[1] After simplifying we obtain : 
[2] 
