I am trying to solve an ODE of the form: (d/dt) x = A * x
given the square matrix A and the vector x at t=0 in sympy. The system I am studying has more than 50 equations.
As I defined it above, I believe these equations are linear, homogeneous, and first-order. When I looked in the sympy documentation, I found something similar ("system_of_odes_linear_neq_order1_type1"). I defined the system and am trying to solve with a command like so:
sympy.dsolve(system,hint='system_of_odes_linear_neq_order1_type1')
The script has been running for a while without terminating so I'm getting a bit worried. On second look, I saw the system being called "nonhomogeneous" in the documentation:
https://www.cfm.brown.edu/people/dobrush/am33/SymPy/part2.html#sympy.solvers.ode._linear_neq_order1_type1
Why is it called "nonhomogeneous" here? Is type of solver I used incorrect and should I redefine the system/solver? I don't see many other options for systems of differential equations where there are more than 3 equations.