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Variation of parameters problem, very BIG, but i think i'm right so far! Diff EQ

  1. Feb 20, 2006 #1
    OKay everyone, this is a big f'ing problem (to me anyways) and its only worth 1 point! But i'm doing it anyways. So here was my attempt, everything seems to be working out like it should but look at what u1 came out too, what am i going to do with that mess? Also do u see any mistakes? Thanks!
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  2. jcsd
  3. Feb 20, 2006 #2

    quasar987

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    That IS a lot of work. Are you sure that's how you're expected to solve these problem? Our friend Lagrange cooked up a crispy formula just for these occasions. It says that if [itex]y_1(t)[/itex] and [itex]y_2(t)[/itex] are linearly independant solution to the homogeneous equation y'' + p(t)y' + q(t)y = 0, then a particular solution to the inhomogeneous equation y'' + p(t)y' + q(t)y=g(t) is

    [tex]Y(t) = -y_1 \int \frac{y_2 g}{W(y_1,y_2)}dt + y_2\int\frac{y_1 g}{W(y1,y_2)}dt[/tex]
     
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