Developing ODE from data?

https://pdfs.semanticscholar.org/dd6d/8da4114de390fe5190a8aa0b25c6a99f935c.pdf In the first example of this link I understand the methods used but what I don’t understand is how or why they assumed second order. Is it because it oscillated so that indicates second order due to change in concavity? So if my data... show more https://pdfs.semanticscholar.org/dd6d/8da4114de390fe5190a8aa0b25c6a99f935c.pdf

In the first example of this link I understand the methods used but what I don’t understand is how or why they assumed second order. Is it because it oscillated so that indicates second order due to change in concavity?

So if my data doesn’t oscillate and represents something more along the lines of half of a parabola does that mean I would only estimate the first derivative using finite differences?

I’m trying to obtain an equation to model the loss of CO2 from my can over time so as you can picture it, at t=0 the cO2 is high and eventually falls to 0 or atmospheric conditions. Those are my boundary conditions and initial conditions. But my cans initial concentration of co2 can change so ultimately I want a function where I can input the initial concentration then it can model the loss over time for me.

I’m teaching myself as I go off the internet so it’s confusing but I feel like I understand how to fit curves from what I’ve read and solve for coefficients for that particular data set but I’m wondering how to develop a model with everything already solved and just needs the initial condition as an input and it will model it
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