Simple short question on differentials

Dec 2015
1,085
169
Earth
Does the equation below have an integrating factor? If not, why? If yes, why?
\(\displaystyle X''+p(x)X'+q(x)X=f(x)\)
 
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SDK

Sep 2016
804
545
USA
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.
 

mathman

Forum Staff
May 2007
6,933
775
Integrating factors can be used in general for first order equations. For higher order some work will be required.