Solving ODE with Data Points: Finding Equation and Integrating Method

[RagincajunLA]

hey guys, i was given some data points and i had to find an equation to fit the model. now my differential equation is h'= ah^b - ch^d with b < 0. I can't find any method for integrating because i don't know the constants in the equation. but i have the data points so that must help somehow. i also know the maximum and minimum of the data points. someone please help me figure out how to integrate this.

 

[K^2]

If your task is to find constants a, b, c, and d, such that h(t) satisfying dh/dt = ah^b - ch^d fits the given points (h_i, t_i), then finding general solution to h(t) might be a backwards way of doing things.

There exist methods for finding a derivative of a function at a point given some discrete data set. These are approximate, but they essentially assume that your data is a high-order polynomial, and the solution to your ODE can be at least approximated with one.

So, use your set of h_i and t_i to find estimates for h'_i. Now you have a standard non-linear fitting problem f(h_i,a,b,c,d) = h'_i. There are a number of ready algorithms and programs that can take care of both steps.

 

[dgOnPhys]

Otherwise if you are daring you can try wolframalpha.com [integrate 1/(a*x^b - c*x^d)]. Spoiler: you'll have to like the hypergeometric function