I’m doing experimental data in a chemistry lab and I have faced this mathematical problem at a point of my work. Hope you guys can help me with that. What would be the best way to find two constants m and n for an equation:

$\ln\frac{ \frac{dx}{dt}}{x^m(1-x)^n}=c$

where $c$ is a constant, $x$ is changing with $t$ (both $x$ and $t$ are experimentally obtained values)

An example of $t$ and $x$ relation:

 t        x
5.58    0.1302
8.75    0.1901
11.92   0.2402
15.10   0.2793
18.28   0.3121

My knowledge in calculus methods isn't very good. If you can advise me towards a method that can apply to this case, that would be very helpful. Many thanks,


You can solve this differential equation, the answer is an incomplete beta function $B_x(1-m,1-n)=(t-t_0)e^c$. This give another unknown $t_0$ which you may be able to fix, maybe you know that x=0 when t=0 or something, otherwise you need to use the data. You can use the website wolframalpha to give you values of this function. If you think m and n are small I would just try plotting some possibilities.

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