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Solving Differential Equation System

  1. Feb 10, 2012 #1
    1. The problem statement, all variables and given/known data
    x`=z-y
    y`=z
    z`=z-x
    x(0)=1; y(0)=1; z(0)=1




    3. The attempt at a solution
    Would be glad to know the steps I need to take.
     
  2. jcsd
  3. Feb 10, 2012 #2

    ehild

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    Gold Member

    Hi Sergej,

    This is a system of first order linear differential equations. Have you learned about them?


    ehild
     
  4. Feb 11, 2012 #3

    ehild

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    Seek the solutions in the form

    x=Aeλt
    y=Beλt
    z=Ceλt.

    You get a "characteristic equation" for λ, with 3 solutions, real and complex. Substitute back and find A,B,C for all cases. The general solution is a linear combination of these three, match the constants to the initial conditions.


    ehild
     
  5. Feb 11, 2012 #4

    HallsofIvy

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    There are a number of different ways to solve linear systems of equations. If you show no work at all, we have no idea which method you have learned and what help would be appropriate. One method is to write the system as a matrix equation. Can you do that? Another would be to differentiate the equations, eleminating variables until you have a third order equation in a single variable. Have you done that in class?
     
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