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Math Help - Second order ordinary differential equation.......

  1. #1
    Newbie
    Joined
    Feb 2011
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    1

    Second order ordinary differential equation.......

    this is really annoying as i dont know what this question is asking and this coursework is in for TOMORROW
    its only worth 3 marks out of 50 so it makes me feel dumb....

    anyway the question is:

    du^2/dx^2 + 2(du/dx) + x.u = (x^2 - 2)e^-2(x-1)

    it says rewrite as a system of first order differential equations

    what does THIS MEAN??

    any help appreciated
    thanks
    Marek
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  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    We may write

    <br />
\displaystyle<br />
\frac{du}{dx}=v<br />

    and the initial equation becomes

    <br />
\displaystyle<br />
\frac{dv}{dx}=-2v-xu+(x^2-2)e^{-2(x-1)}<br />
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