Curve fitting differential equations in Python
Certainly you intend to have the third derivative on the right. 
Group your data in relatively small bins, possibly overlapping. For each bin, compute a cubic approximation of the data. From that compute the derivatives in the center point of the group. With the derivatives of all groups you now have a classical linear regression problem.
If the samples are equally spaced, you might try to move the problem into frequency space via FFT. A sensible truncation of the data might be a problem here. In the frequency space, the task reduces to a polynomial linear regression.
I have a curve of >1000 points that I would like to fit to a differential equation in the form of x'' = (a*x'' + b x' + c x + d), where a,b,c,d are constants. How would I proceed in doing this using Python 2.7?