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Math Help - tricky little first order linear DE

  1. #1
    RF7
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    tricky little first order linear DE

    see if you can get this one.

    y'=y-t^-2+t^-3-t^-1

    t>0

    No integration tables, please. And no computers. Thanks for looking and do tell if you can solve this one!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by RF7 View Post
    No integration tables, please. And no computers. Thanks for looking and do tell if you can solve this one!
    Using the standard method:

    (a) The general solution for y'-y=0 is y=Ce^t .

    (b) Tryng solutions of the form y=C(t)e^t for the complete we obtain:

    y=e^t\left(\displaystyle\int \dfrac{e^{-t}(1-t-t^2)dt}{t^3}+C\right)

    So, no integration tables and no computer.

    Regards.

    Fernando Revilla
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  3. #3
    RF7
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    Yes, there it is, in integral form. I don't think this one can be solved without integral form.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by RF7 View Post
    I don't think this one can be solved without integral form.
    Right, it can't be solved in terms of elementary functions.

    Regards.

    Fernando Revilla
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  5. #5
    RF7
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    Thanks for the help, Fernando~
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