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Math Help - Nonlinear Differential Equation

  1. #1
    Newbie Assassin0071's Avatar
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    Nonlinear Differential Equation

    The Question is:

    Solve the following equation. The constant \mu is non negative and h is greater than zero.

    { ( \frac{dr}{dt} ) }^2 = \frac{2\mu}{r} + 2h

    Any help would be apperciated as I'm not entirely sure where to start with this problem.
    Last edited by Assassin0071; October 13th 2012 at 04:36 PM.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Nonlinear Differential Equation

    Most likely, solution looks like:

    \frac{\mu  \text{Log}\left[h \sqrt{r}+\sqrt{h} \sqrt{\mu +h r}\right]}{h^{3/2}}-\frac{\sqrt{r} \sqrt{\mu +h r}}{h} = \pm \sqrt{2} t+\text{C1}
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  3. #3
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    Re: Nonlinear Differential Equation

    Hi Assassin0071 !
    In fact, it is an ODE with separable variables :
    dr/dt = sqrt((2m/r)+2h) = sqrt((2m+2hr)/r)
    dt = dr/sqrt(r/(2m+2hr))
    Then, integrate it.
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