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Homework Help: Variation of Parameters on a system of Differential Eqs (Simple question)

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Okay so when solving a system of D.E.s using Variation of Parameters I know that first I find the complementary solution Xc and then do a bunch a of crap after that using the fundamental matrix.

    Now I just came across a problem with repeated roots, so I just want to clarify that I am correct in saying that if the complementary solution looks like this:

    [tex]X_c=c_1\left(\begin{array}{c}1\\1\end{array}\right)+c_2[\left(\begin{array}{c}1\\1\end{array}\right)t+\left(\begin{array}{c}1\\0\end{array}\right)][/tex]


    Then the fundamental matrix looks like this:

    [tex]\Phi(t)=\left(\begin{array}{cc}1 & t+1\\ 1 & t\end{array}\right)[/tex]



    Just a yes or no will do..... (if it's no, I am in trouble!)

    Thanks!!
     
  2. jcsd
  3. Apr 27, 2008 #2
    Anyone? I just want to make sure before I go using this....
     
  4. Apr 27, 2008 #3
    Well I thought it was a simple question.....
     
  5. Apr 27, 2008 #4
    Tina.... eat the food!
     
  6. Apr 28, 2008 #5
    eat the food!
     
  7. Apr 28, 2008 #6

    HallsofIvy

    User Avatar
    Science Advisor

    Does it help you to point out that

    [tex]\left(\begin{array}{cc}1 & t+1\\ 1 & t\end{array}\right)\left(\begin{array}{c}c_1 \\ c_2\end{array}\right)= \left(\begin{array}{c}c_1+ c_2(t+1) \\ c_1+ c_2t\end{array}\right)[/tex]
     
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