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Math Help - differencial equation

  1. #1
    Member billym's Avatar
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    differencial equation

    <br />
v \frac{dv}{dx} = -\frac{g}{b^2}(v^2 + b^2)<br />

    I have:

    <br />
ln|v + 1| = - gx + C<br />
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by billym View Post
    <br />
v \frac{dv}{dx} = -\frac{g}{b^2}(v^2 + b^2)<br />

    I have:

    <br />
ln|v + 1| = - gx + C<br />
    1. you have no dependence on b so its unlikeley to be right.

    2. \frac{v}{v^2+b^2}~\frac{dv}{dx}=-\frac{g}{b^2}

    so (assuming g and b are constants):

    \log (v^2+b^2)=-\frac{2g}{b^2}x+C

    RonL
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by billym View Post
    <br />
v \frac{dv}{dx} = -\frac{g}{b^2}(v^2 + b^2)<br />

    I have:

    <br />
ln|v + 1| = - gx + C<br />
    \int \frac{v}{v^2+b^2}dv=\frac{1}{2}\ln|v^2+b^2|
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  4. #4
    Flow Master
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    Quote Originally Posted by CaptainBlack View Post
    1. you have no dependence on b so its unlikeley to be right.

    2. \frac{v}{v^2+b^2}~\frac{dv}{dx}=-\frac{g}{b^2}

    so (assuming g and b are constants):

    \log (v^2+b^2)=-\frac{2g}{b^2}x+C

    RonL
    Alternatively, reply #6 in this thread would provide the answer.
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