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Sorry, I'm not entirely sure how to define this differential equation in python.

enter image description here

I understand there is a equation inside the equation, but how would you define this differential equation of natural log?

The above equation stems off of the actual Halo Mass Function

enter image description here

Edit: I'm trying plot this equation of given information of M's in the form of a structured array, not solve it. This is a equation inside of another equation that's called the Halo Mass function. It plots masses basically. So in this case, i'm trying to plot it. Hence, me asking how to define it.

iron2man
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    Possible duplicate of [Differential Equations in Python](http://stackoverflow.com/questions/5847201/differential-equations-in-python) – hdost Dec 01 '15 at 02:39
  • In that case, i do not have initial conditions. This is a function inside the Halo Mass function. The point of this equation will play is graphing masses of Halo masses. I guess I should edit my question to be more elaborate. – iron2man Dec 01 '15 at 02:55
  • Could you state what supposed to be an abscissa, and what supposed to be an ordinate, and what would be fixed parameters (plot Y vs X for a given A, B, C, ...) – Severin Pappadeux Dec 01 '15 at 04:08
  • @Severin Pappadeux Yes, sorry about that. The Abscissa (M) and ordinate , the left part of the function, is based off of the original equation. But not to sound frank, i'm just curious on how you define the equation d(ln\sigma)/d(lnM) in defintion. – iron2man Dec 01 '15 at 04:35
  • @DarthLazar well, d\log(M)/dM = 1/M, thus d\log(M) = dM/M. But why you want to deal with d(ln\sigma)/d(lnM)? `\log()` is monotonical function, so you could just use \log(M) as abscissa, it doesn't matter. So basically you have new `x=\log(M)`, equation in the form df/dx = `some integral`, and you want to plot it? Just compute integral, that's it, for each `x` – Severin Pappadeux Dec 01 '15 at 04:57
  • http://stackoverflow.com/questions/15928750/numerical-ode-solving-in-python?rq=1 – hdost Dec 01 '15 at 16:45
  • @hdost no, he is not trying to solve it, my guess of the moment is this is implicitly defined function which should be plotted – Severin Pappadeux Dec 02 '15 at 03:56

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