Help solving differential equation

[timsea81]

Hello!
I am looking for someone's help solving a differential equation. In the attached image:

A, B, C, and D are all constants
x = x(t)

This is one step in the process for my thermo assignment. Using Matlab or some other ODE software would be an acceptable way to solve the problem if there is no easy way to do it by hand. Any help you could lend would be appreciated. Thanks.

 

[hunt_mat]

I would look at the differential equation in the following form:
$$C\frac{dt}{dx}+\frac{Dt}{x-B}=\frac{A}{x^{2}}$$
This looks to be some kind of integrating factor equation (I could be wrong) but have a go.

 

[timsea81]

Thanks, I'll go down that road in a minute but first I have another question that I will post as a separate question as it is unrelated.

 

[JJacquelin]

Hi !

The ODE is linear and can be solved as t=t(x)
The function t(x) is related to a Gauss hypergeometric fonction, or alternatively a Beta function : attached document.
The function x(t) cannot be expressed with a finite number of elementary functions.
x(t) have to be compuded thanks to numerical methods (But, for some particular values of the constant coefficients, it could be expressed analytically).