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I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few pages of the book.

I am having issues with going from Equation 2.51 to 2.52. Can anyone please help with this, i.e. give a step by step solution?

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Mitradip Das
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Set the left hand side of 2.50 to zero which is what "dropping the second derivative on the left hand side" means and solve for dx/dt.