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Wronskian problem

  1. Feb 28, 2005 #1
    [tex]w[f,g](t)= t^2\exp{t}\\f(t)=t[/tex]

    Thats what i get, the problem is to find g(t)

    So, i start; f'(t)=1

    [tex]w[f,g](t)= t^2\exp{t}=f(t)g'(t)-f'(t)g(t)\\t^2\exp{t}=tg'(t)-g(t)[/tex]

    divide by t,

    [tex]t\exp{t}=g'(t)-\frac{g(t)}{t}[/tex]

    its a 1st order linear eq. I solve for the integrating factor and get t. i multiply through and reduce

    [tex](tg(t))'=t^2\exp{t}[/tex]

    then i integrate with the product rule and get

    [tex]tg(t)=t^2\exp{t}+2t\exp{t}+C[/tex]

    divide by t and get

    [tex]g(t)=t\exp{t}+2\exp{t}+\frac{C}{t}[/tex]

    which is wrong. The answer in the book is

    [tex}t\exp{t}+Ct[/tex]

    not sure where i went wrong, i know its probably something dumb, but its late, so i need help.

    ~gale~
     
  2. jcsd
  3. Feb 28, 2005 #2

    Hurkyl

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    I don't like your integrating factor. When you expand out (t g(t))', you don't get the right thing.
     
  4. Feb 28, 2005 #3
    mk, well, the int factor is

    [tex]e^{\int{1/t}dt}{[/tex]

    right? so the exponential and log cancel and t is all that's left... how's that wrong?

    ( i can't get the latex right on that, hope you get what i mean)
    (also, i accidently posted twice, you can delete the other one... i dunno how)
     
    Last edited: Feb 28, 2005
  5. Feb 28, 2005 #4
    oh i just realized, its supposed to be

    [tex]e^{-\int{\frac{1}{t}dt}[/tex]

    i forgot about that negative sign.
    which makes my int factor 1/t which changes absolutely everything and makes the problem right.... AUGH, DAMNED NEGATIVES.... grr. thanks...
     
  6. Mar 1, 2005 #5

    HallsofIvy

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    I really wish people would not post the same thing twice! I just posted a reply to the OTHER "Wronskian problem" before I saw that it had already been settled here.
     
  7. Mar 1, 2005 #6
    i said sorry... i didn't mean to, and i couldn't delete it.... :frown:
     
  8. Mar 1, 2005 #7

    dextercioby

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    I hope you've got the point.No double posting...:rolleyes:You should have PM-ed a (preferably online) mentor/admin.He would have deleted the thread.

    Daniel.
     
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