What is the python code for these differential equations? We have the octave code for each, but we need it in python.

1. From 1985 to 1995 in the Yellowstone national park, the elk population in the park increased by 40% , from 13.000 to 18.000 . In year 1995, wolves were released in the park and and til 2009 the elk population fell from 18.000 to 7000. The model for the population dynamics is :

In this equation, E(t) represents the elk population (in thousands) where t is measured in years since 1985. The solution finds the combined birth/death growth rate r to be approximately 0.0325 yielding:

Octave:

>> function xdot = f(x,t) r=0.0325;

xdot(1) = r*x(1);

endfunction

>> x = 1sode (f, [13]. (t = 1inspace (0, 50, 200)));

>> plot (t,x)

2. In 1995, 21 wolves were initially released and their numbers have risen. In 2007, biologists estimated their number to get to 171.

We need to solve this system of equations in Python.

Octave :

>> function xdot = f(x,t)

xdot(1) = 0.0325 * x(1) - 0.8 * x(1) * x(2);

xdot(2) = -0.6 * x(2) + 0.05 * x(1) * x(2);

endfunction

>> x = 1sode (f, [18; 0.021], (t = 1inspace (0, 50, 200)));

>> plot (t,x)

E(0) = 13.0, E (10) = 18.0 E(t) = 13.0 x 0.0325 de dt = = 0.0325 E - 0.8EW W = -0,6W + 0.05 EW dt E(0) = 18.0,W(0) = 0.021