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Math Help - Euler Differential Equation

  1. #1
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    Exclamation Euler Differential Equation

    Ok I have the equation:

    theta^2(d2R/dtheta2)+3theta(dR/dtheta)-8R=20(theta^-3)

    The condition is that R=10 when theta=1

    I have worked out the equation as far as the General Solution.

    The C.F i got was Ae^2t + Be^-4t

    I then got a General Solution of Ae^2t + Be^-4t - 4e^-3t

    How do I find the values of A and B ?
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  2. #2
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    Quote Originally Posted by LooNiE View Post
    Ok I have the equation:

    theta^2(d2R/dtheta2)+3theta(dR/dtheta)-8R=20(theta^-3)

    The condition is that R=10 when theta=1

    I have worked out the equation as far as the General Solution.

    The C.F i got was Ae^2t + Be^-4t

    I then got a General Solution of Ae^2t + Be^-4t - 4e^-3t

    How do I find the values of A and B ?
    You have the condition \theta (1) = 10.
    Where is your condition \theta ' (1) = ?.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    You have the condition \theta (1) = 10.
    Where is your condition \theta ' (1) = ?.
    R is finite as theta tends to infinity.
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  4. #4
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    Quote Originally Posted by LooNiE View Post
    R is finite as theta tends to infinity.
    Okay. You said you got the general solution of Ae^{2\theta} + Be^{-4\theta} - 4e^{-3\theta}.
    For this to stay bounded as \theta \to \infty you need A=0.
    Do you see why?
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  5. #5
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    Quote Originally Posted by ThePerfectHacker View Post
    Okay. You said you got the general solution of Ae^{2\theta} + Be^{-4\theta} - 4e^{-3\theta}.
    For this to stay bounded as \theta \to \infty you need A=0.
    Do you see why?
    yes i see. but how do i find B?
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  6. #6
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    Quote Originally Posted by LooNiE View Post
    yes i see. but how do i find B?
    Once you let A=0 you are let with Be^{-4\theta} - 4e^{-3\theta}.
    You are told that this expression is equal to 10 with \theta = 1.
    Thus, Be^{-4} - 4e^{-3} = 10.

    Now solve for B.
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