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Thread: Insanely hard differential equation

  1. #1 Insanely hard differential equation 
    Member iopst's Avatar
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    I'm trying to find the equilibrium size of a planetesimal which is made of a material whose density is pressure dependent. (quite a mouthful)

    I have to solve this differential equation:



    where a and b are constants.


    Unfortunately, I don't know how to start.
    "It's not the facts that are important, but the way we think about them."

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  2. #2  
    Administrator Markus Hanke's Avatar
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    Was this equation given in an exercise, or did you come up with it yourself ?
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    Member iopst's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Was this equation given in an exercise, or did you come up with it yourself ?
    I came up with it myself. The relationship between pressure and density was not based on any real material but just something I made up.
    "It's not the facts that are important, but the way we think about them."

    - W. Lawrence Bragg
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  4. #4  
    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by iopst View Post
    I came up with it myself. The relationship between pressure and density was not based on any real material but just something I made up.
    Ok, I see.
    The differential equation as it stands here is unlikely to be solvable in closed analytic form; I'd say your best bet would be to attempt a numerical solution using one of the numerous approaches and/or software intended for cases just like this one. Perhaps you could start off with CAM software such as MAPLE or Mathematica, and see where that leads you.
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  5. #5  
    Member iopst's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Ok, I see.
    The differential equation as it stands here is unlikely to be solvable in closed analytic form; I'd say your best bet would be to attempt a numerical solution using one of the numerous approaches and/or software intended for cases just like this one. Perhaps you could start off with CAM software such as MAPLE or Mathematica, and see where that leads you.
    Yeah, that seems like the only way out.

    I didn't intend for the resulting equation to be so damn complicated, but after plugging everything in it turned out like that.
    "It's not the facts that are important, but the way we think about them."

    - W. Lawrence Bragg
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