0
$\begingroup$

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,

$\endgroup$
2
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.