The second-order differential equation

import numpy as np

from scipy.integrate import odeint

dy1dt = (t * np.exp(t) - y1 + 6 * y0) / 9

return [dy0dt, dy1dt]

t = np.linspace(0, 2, 100) # Adjust the time span as needed

# Solve the differential equation

plt.plot(t, y_solution)

plt.xlabel('t')