Show how to speed up scipy.integrate.odeint simply by decorating the right-hand side with numba's jit function

NumbaODEExample.ipynb

I wrote a wrapper to LSODA which has no overhead: https://github.com/Nicholaswogan/NumbaLSODA . During an ODE solve, the python interpreter is never used, so everything is fast for small problems:

from NumbaLSODA import lsoda_sig, lsoda
import numba as nb

@nb.cfunc(lsoda_sig)
def RHS_nb(t, y, dy, p):
    dy[0],dy[1] = t*y[1],y[0]

funcptr = RHS_nb.address

@nb.njit()
def test():
    sol, success = lsoda(funcptr, y0_, t)
    
y0_ = np.array(y0)
%timeit test()

result is

26.2 µs ± 342 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)