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June 29th, 2018, 12:34 PM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 316 Thanks: 42  Simple short question on differentials
Does the equation below have an integrating factor? If not, why? If yes, why? $\displaystyle X''+p(x)X'+q(x)X=f(x)$ Last edited by skipjack; June 29th, 2018 at 11:20 PM. 
June 29th, 2018, 12:56 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 531 Thanks: 304 Math Focus: Dynamical systems, analytic function theory, numerics 
Answer is yes because it is a linear equation and every linear equation has a solution by integrating factor method. Sometimes this is called the variation of constants method when applied to higher order equations but they are exactly the same method.

June 29th, 2018, 02:27 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,660 Thanks: 647 
Integrating factors can be used in general for first order equations. For higher order some work will be required.


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