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Math Help - Confusion With A Separable Differential Equation

  1. #1
    Junior Member
    Joined
    Jan 2010
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    Confusion With A Separable Differential Equation

    Several times now, I have ended up with the incorrect answer for this differential equation:

    \frac {dB} {dt} + 5B = 40

    With starting conditions: B(1) = 70. Here is how I've approached it:

    \frac {dB} {dt} = 40 - 5B = 5(8-B)

    \frac {dB} {8-B} = 5 dt

    ln(8-B) = 5t + C

    8-B = Ce^{5t}

    B = 8 - Ce^{5t}

    So for the initial starting conditions:

    70 = 8 - Ce^5

    \frac {62} {e^5} = -C

    And so B = 8 + \frac {62} {e^5}e^{5t}

    I appreciate if anyone can guide me as to where I went wrong. Thanks for the help.
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  2. #2
    Junior Member
    Joined
    Mar 2010
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    Hi Spudwad,

    There should be minus sign here because of \frac{d\ln(8-B)}{dB}=-\frac{1}{8-B},
    So yu will get,

     (-1) \ln{(8-B)} = 5t + C

     \ln{(8-B)^{-1}} = 5t + C

    Try with this. If you still get problems, write again
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