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Homework Help: Systems of first order linear equations involving wronskian and matrices

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    If y3(0) = 2y2(0) - y1(0), what is W(3)?

    2. Relevant equations

    [itex]\frac{d}{dt}[/itex] y(t) = A(t) y(t),

    A(t) =
    [1 et e-t]
    [e-t 0 et]
    [2 sin(t) -1]

    3. The attempt at a solution

    I already solved the Wronskian W(t)=c*e∫(1+0-1)dt=c

    What I was not sure about was how to go about solving for the general solution of the y's.

    Would it be y3(t)=eAt*y3(0)?

    y3(t)=eAt*(2y2(0) - y1(0))
    where At =
    [t tet te-t]
    [te-t 0 tet]
    [2t tsin(t) -t]
     
  2. jcsd
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