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Math Help - how to find a solution the differential equations

  1. #1
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    how to find a solution the differential equations

    Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
    How would I do this?
    Thank everyone.Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
    How would I do this?
    Thank everyone.
    how to find a solution the differential equations-33333.jpg
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  2. #2
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    Re: how to find a solution the differential equations

    It's not clear to me what you are asking, or what the number of equations has to do with it.
    But, it is true that, first, most differential equation do not have "analytic" solutions and second, even for those that do, you typically need to use very different solutions methods for different equations.
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  3. #3
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    Re: how to find a solution the differential equations

    Quote Originally Posted by mulyak View Post
    Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
    How would I do this?
    Thank everyone.Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
    How would I do this?
    Thank everyone.
    Click image for larger version. 

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    The last equation, the constraint, is irrelevant since P_{16} does not appear in the earlier differential equations.

    The first 15 equations constitute a linear constant coefficient first order system and can be written:

    \frac{d}{dt}{\bf{P}}={\bf{AP}}

    which has general solution {\bf{P}}={\bf{K}\exp({\bf{At}})

    .
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