SymPy/SciPy: solving a system of ordinary differential equations with different variables

Question

I am new to SymPy and Python in general, and I am currently working with Python 2.7 and SymPy 0.7.5 with the objective to: a) read a system of differential equations from a

Answer 1

If you are going to solve the system in the same script that reads the file (so systemOfEquations is available as a global variable), and if the only variables used in systemOfEquations are x, y and possibly t, you could define dX_dt in the same file like this:

def dX_dt(X, t):
    vals = dict(x=X[0], y=X[1], t=t)
    return [eq.evalf(subs=vals) for eq in systemOfEquations]

dX_dt can be used in odeint. In the following ipython session, I have already run the script that creates systemOfEquations and defines dX_dt:

In [31]: odeint(dX_dt, [1,2], np.linspace(0, 1, 5))
Out[31]: 
array([[ 1.        ,  2.        ],
       [ 1.00947534,  1.90904183],
       [ 1.01905178,  1.82223595],
       [ 1.02872997,  1.73939226],
       [ 1.03851059,  1.66032942]]