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September 17th, 2013, 06:37 AM  #1 
Member Joined: Nov 2010 Posts: 36 Thanks: 0  Quick question: Coupled first order differentials, correct?
I am given the following second order differential equation. I am wondering whether my final x'=ax+f(t) equation is correct? +K(zu)=0" /> Putting all u terms on the right side: Substituting using: This gives me two first order differential equations: This can ultimately be written in the form: Is it correct to put u' and u in the f(t) part of the equation? Despite knowing that a second order D.E. can only be replaced by two first order D.E's, I have my doubts that I should also substitute u' with another term to have a third first order D.E. 
September 17th, 2013, 07:31 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Quick question: Coupled first order differentials, corre
The question is really about your first equation, "Mz''+ B(z' u')+ K(z u)= 0". What is "u"? Is it a given function or an unknown function you have to determine? If it is a given function then "Bu'+ Ku" is just another function and what you have done is perfectly valid.


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