human
I am working on the file "Numerical Integration Tutorial.ipynb".
The first task is:
Congratulations: you are now ready to integrate any system of differential equations! (We hope generalizing the above to more than 2 equations won't be very challenging).
Exploring parameters with a simple interface
IPython’s widgets allow to create user interface (UI) controls for exploring your code interactively. To use this resource you have to run the code below in a computer with all the software required (see first section), plus the library ipywidgets.
The interact function provides a quick way to use widgets to explore the parameter space of ODEs. To do this, first create a new function that integrate your ODEs and return a plot. The argumnts of this functions should be the parameters that you want to explore.
Can you write Python program for it?
assistant
#Here is the Python program you requested.

def LV_plot(r=2, c=0.5, e=0.5, d=1):
    # Time range
    t = arange(0, 50., 0.01)
    # Initial conditions
    x0 = array([1., 3.])
    # The function to be integrated
    def LV(x, t, r, c, e, d):
        return array([ r*x[0] - c * x[0] * x[1],
        e * c * x[0] * x[1] - d * x[1] ])
    #integrating
    y = odeint(LV, x0, t, (r, c, e, d))
    # ploting: use the function show
    show(plot(t, y))