Transform to system of first order equations

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To transform the third-order differential equation u''' - 8u'' + 2u' - 3u = 0 into a system of first-order equations, the user defines new variables: x1 = u, x2 = u', and x3 = u''. This leads to the relationships x1' = x2, x2' = x3, and x3' = u'''. The user is unsure how to express the third derivative in terms of the new variables and seeks clarification on substituting back into the original equation. The discussion highlights the challenge of transitioning from second-order to third-order equations in this context. Understanding these transformations is crucial for solving higher-order differential equations effectively.
Taylor1234
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Homework Statement


u'''-8u''+2u'-3u=0


Homework Equations





The Attempt at a Solution


So I let:
x1 = u
then x1' = u'
x2 = u'
then x1' = x2
and x2' = u''
x3 = u''
then x2' = x3
and x3' = u'''

I have only done these problems with second order equations, so I don't understand which values I am supposed to plug back into the original equation. Any help is appreciated! Thanks!
 
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