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).

 

[blue_raver22]

Hello! I would be happy to help you with your differential equation. Differential equations can be quite challenging, but with the right tools and techniques, they can be solved effectively. Can you provide more information about the specific equation you are trying to solve? What is the equation itself, and what are the values of A, B, C, and D? This will help me understand the problem better and provide you with a more accurate solution. In the meantime, I would recommend using a software like Matlab to solve the equation, as it can handle complex equations and provide accurate solutions. Let me know if you have any further questions or if you need any additional assistance. Best of luck with your thermo assignment!