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Math Help - Linear System of Equations

  1. #1
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    Linear System of Equations

    I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

    u'\; =\; 4u\; -\; v
    v'\; =\; -4u\; +\; 4v

    Where v and u are dependent over x.
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  2. #2
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    Quote Originally Posted by jameselmore91 View Post
    I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

    u'\; =\; 4u\; -\; v
    v'\; =\; -4u\; +\; 4v

    Where v and u are dependent over x.
    If you go to Chris' tutorial (the sticky at the top)

    http://www.mathhelpforum.com/math-he...-tutorial.html

    on page 12 you'll find what you need.
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  3. #3
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    Quote Originally Posted by jameselmore91 View Post
    I'm having some trouble with Linear Systems of Equations, I get the basic concept but it would be helpful if someone could do the following problem step by step.

    u'\; =\; 4u\; -\; v
    v'\; =\; -4u\; +\; 4v

    Where v and u are dependent over x.
    The most fundamental way to do this is to differentiate the first equation again gettin u''= 4u'- v'. From the second equation, v'= -4u+ 4v so we can replace it: u''= 4u'- (-4u+ 4v)= 4u'+ 4u- 4v. We still have a "v" to eliiminate but from the first equation, v= 4u- u' so that becomes u''= 4u'+ 4u- 4(4u- u')= 8u' -12u. that is, u''- 8u+ 12u= 0. Solve that equation for the general solution, u, then use v= 4u- u' to find v.
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