How to solve a system of equations mixing non-linear ODE and non-linear "simple" equations?

I have a system that I want to solve numerically (attached an overview of the form, X1, X2, etc. are the variable, while C1, c2, etc. are constants). I know a bit about how to solve ode with ode45; I also have some ideas about solving common "simple" equations. But in this system, that describes a dynamic of a process, not all equations are ODE; so, I have some challenges with the structure/syntax of ode45. Please, would you shar with me some ideas about how to solve this kind of system with Matlab or simulink?

Thank you.

Answer 1

[Ayham Aljawabrah]

The solvers usually able to solve index-1 DAE, not all the equations are apperent but you have too many variables you mostly need to reduce the order of your differential algebraic equation (DAE) system.

The below link shows how to symbolic math toolbox to prepare a DAE system to be solved with Matlab ode solver ode15i, ode15s, ode23s can handle DAE, the link below utilize ode15i

https://www.mathworks.com/help/symbolic/solve-differential-algebraic-equations.html

For more info about DAE, check the below link https://www.mathworks.com/help/matlab/math/solve-differential-algebraic-equations-daes.html

[NECK]

Dear Ayham. Thank you for your quick feedback. My aim is not so solve the problem symbolicly but numerically. Or the idea is to try to "rewrite" the system using the symbolic tool and then solve the obtained system numerically?

[Ayham Aljawabrah]

Yes, the procedure is to use symbolic toolbox to rewrite the system in a way that the numerical solver can solve it.

[NECK]

Ok, thank you. I will try that option and provide a feedback.