Pls check the following links hope you find solution to your problem

1. https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Book%3A_Chemical_Process_Dynamics_and_Controls_(Woolf)/02%3A_Modeling_Basics/2.07%3A_Solving_ODEs_with_Mathematica-_How_to_find_numerical_and_analytical_solutions_to_ODEs_with_Mathematica

2. https://www.cfm.brown.edu/people/dobrush/am33/Mathematica/index.html

Hi, why do you mean by "coefficients are not numbers"? If these coefficients are parameters, you can use MATHEMATICA or MAPLE to find an analytical solution to your system of ODEs. As suggested by Salawudeen, you should simply have a look to the corresponding documentation. Best

this should help:

https://reference.wolfram.com/language/howto/SolveADifferentialEquation.html

What happens is that you want to find the equation based on those coefficients. That is, you want to find a general formula. With "wolfram mathematica" it can be solved as long as the values of these coefficients are known beforehand. I am new to this program, maybe if possible. Thanks.

Manipulating mathematical expressions (for example, calculating the derivative of a mathematical function) and giving the result in the form of a mathematical expression is defined as formal calculation or symbolic calculation. The main software of this kind are:

1) Maple

2) Mathematica

and to a lesser extent:

3) Magma

4) SageMath

Obviously, these softwares require some learning.

They solve many types of differential equations by formal calculation.

I may suggest you to solve the equations using ritz method or galerkin technique by assuming some weighted function that satisfy your boundary conditions