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Math Help - seperable differential equation

  1. #1
    Newbie
    Joined
    Oct 2010
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    5

    seperable differential equation

    \dfrac{dx}{dt} = x^2 + \dfrac{1}{81}

    x(0) = 5

    the answer i got was
    <br />
\dfrac{1}{9} tan( \dfrac{t}{9} + \dfrac{13.94}{9})

    but seems to be wrong and i cant seem to figure out what im doing wrong
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  2. #2
    Senior Member
    Joined
    Mar 2009
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    378
    \dfrac{dx}{dt} = x^2 + \frac{1}{81} \Rightarrow \dfrac{dx}{x^2 + \frac{1}{81}}= dt \Rightarrow \int\!\dfrac{dx}{x^2 + \frac{1}{81}}= \int\!\,dt \Rightarrow 9 \tan^{-1} (9x) = t + c \Rightarrow 9\tan^{-1} 45 = c \dots
    So it appears that your solution is correct.
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