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Math Help - [SOLVED] Rearranging a differential equation

  1. #1
    Bud
    Bud is offline
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    [SOLVED] Rearranging a differential equation

    Hi I am supposed to "just" rearrange the following equation and at one point substitute dh/dt = A/rho with the constant A:


    With the constant C and rho(i).

    The result looks like this:



    I cannot rearrange the 1st equation in a way that I obtain the 2nd. I assume that one has to ibntegrate at one point to get rid of the logarithm though.

    Thanks in advance.

    Cheers
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  2. #2
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    If \rho=f(h) and h=g(t) then \frac{d\rho}{dt}=\frac{d\rho}{dh}\frac{dh}{dt} right? So if we calculate what \frac{d\rho}{dh} is and multiply by the given \frac{dh}{dt}=\frac{A}{\rho}, that would give us \frac{d\rho}{dt}. So what is:

    \frac{d}{dh}\left\{\ln\left(\frac{\rho}{\rho_i-\rho}\right)\right\}

    You can figure that out. Then isolate the \frac{d\rho}{dh} term and then just multiply by \frac{A}{\rho}
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