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September 17th, 2013, 06:37 AM   #1
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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(z-u)=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.
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September 17th, 2013, 07:31 AM   #2
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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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