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    Hey there i'm looking for a solution to the following non-linear first order ODE.

     (\frac{dy}{dx})^2 = Ae^{-y}+By+C

    where A, B and C are constants.

    Any ideas on how to solve this or if it's even got an analytical solution?
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    (Original post by langlitz)
    Hey there i'm looking for a solution to the following non-linear first order ODE.

     (\frac{dy}{dx})^2 = Ae^{-y}+By+C

    where A, B and C are constants.

    Any ideas on how to solve this or if it's even got an analytical solution?
    As to whether this has an analytic form, I fed an example of an equation of this form to Mathematica, and it went away and thought for a while and returned with a simple re-write of the original equation. So, possibly not...
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    (Original post by Gregorius)
    As to whether this has an analytic form, I fed an example of an equation of this form to Mathematica, and it went away and thought for a while and returned with a simple re-write of the original equation. So, possibly not...
    It would be interesting to see whether other similar tools (eg. Maple/Matlab etc.), would have any more luck. (if anyone here has them)
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    (Original post by langlitz)
    Hey there i'm looking for a solution to the following non-linear first order ODE.

     (\frac{dy}{dx})^2 = Ae^{-y}+By+C

    where A, B and C are constants.

    Any ideas on how to solve this or if it's even got an analytical solution?
    Isn't this equivalent to \pm \int \dfrac{dy}{\sqrt{Ae^{-y} + By +C}} = x+D? The integral doesn't look at all hopeful for a solution in terms of elementary functions.
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    (Original post by atsruser)
    Isn't this equivalent to \pm \int \dfrac{dy}{\sqrt{Ae^{-y} + By +C}} = x+D? The integral doesn't look at all hopeful for a solution in terms of elementary functions.
    Yup, that is what Mathematica returns...
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    (Original post by Gregorius)
    Yup, that is what Mathematica returns...
    Yeah, I was just trying to point out to the OP that it's fairly easy to see if it's likely to have a nice solution as it's separable.
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    (Original post by atsruser)
    Isn't this equivalent to \pm \int \dfrac{dy}{\sqrt{Ae^{-y} + By +C}} = x+D? The integral doesn't look at all hopeful for a solution in terms of elementary functions.
    Yep I was just wondering if there were any fancy methods for solving these kinds of equations which I don't know, wolfram alpha is not always foolproof for differential equations

    I will try a numerical method
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    (Original post by langlitz)
    I will try a numerical method
    I suspect that's the only real possibility here, if you need a solution.
 
 
 
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