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Math Help - Need help with a Wronskian problem.

  1. #1
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    Need help with a Wronskian problem.

    If the Wronskian W of f and g is 3e^{4t}, and if f(t<br />
)=e^{2t} find g(t).

    I know we get e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t} which becomes g'(t)-2g(t)=3e^{2t}.

    It is after this that I am getting messed up. I know you use the integrating factor method to solve this, but I am not coming up with the correct answer shown in my book which is g(t)=3te^{2t}+ce^{2t} I know how to solve first order linear questions but apparently I'm doing something wrong. Can someone help please?


    EDIT: I don't need help with this anymore! I realized the mistake I was making
    Last edited by steph3824; March 5th 2010 at 11:12 AM.
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  2. #2
    Member Black's Avatar
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    Ok, so we have

    g'(t)-2g(t)=3e^{2t}.

    So int. factor: e^{-2\int dt}=e^{-2t}. Multiply both sides of the equation by the int. factor to get

    e^{-2t}g'(t)-2e^{-2t}g(t)=\frac{d}{dt}(e^{-2t}g(t))= 3.

    Integrate both sides with respect to t to get

    e^{-2t}g(t)=3t+c \Longrightarrow g(t)=3te^{2t}+ce^{2t}.

    Edit: Oops! Didn't see your edit.
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