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I have a Wronskian Question?If the Wronskian W of f and g is t^2*e^t

  1. Oct 24, 2011 #1
    I have a Wronskian Question?
    If the Wronskian W of f and g is t^2*e^t and if f(t)=t, find g(t).

    I have tried setting up this problem:

    tg'-t'g = t^2*e^t
    tg'-g = t^2*e^t

    Setting up the integrating factor, µ= e^∫-1 --> µ= e^-t
    (e^-t)t*g' - (e^-t)*g = (e^-t)(t^2*e^t)

    so preferably I would want to be able to set up the equation as (fg)' = (e^-t)(t^2*e^t)

    but the derivative of (e^-t)t is not (e^-t).

    The answer is supposed to be te^t+ct
     
  2. jcsd
  3. Oct 25, 2011 #2

    lurflurf

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    Re: Wronskian

    The quotient rule is handy here
    f g'-f' g=f2(g/f)'

    f g'-f' g=t2(g/t)'=t2et
     
  4. Oct 25, 2011 #3
    Re: Wronskian

    I'm still not getting the right answer.

    I get it down to (te^t)(t-1)+ct
     
  5. Oct 26, 2011 #4

    lurflurf

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    Re: Wronskian

    Where are you getting that t-1? It clearly does not belong.
     
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