'''Example of a right-hand side of a system of two differential equations. 
The scipy function scipy.integrate.ode requires the function exactly in this 
form.

Input: 
    t... independent variable (has to be carried along also
                                in autonomous systems as a dummy-variable)
    y... vector of independent variables (list or 1D array)

Output:
    the vector field f as a function of t and y.
    Attention: f has to be a column vector.

Typical call:
    import scipy
    from scipy.integrate import ode
    from python21_1 import f
    r = ode(f)
    r.set_initial_value([0,1], 0)
    r.integrate(r.t + 2*scipy.pi)
'''

def f(t,y):
    return [y[1], -y[0]]