x, y, t = var('x y t')
F = [-3*x - 2*y, 2*x + y]
n = sqrt(F[0]^2 + F[1]^2)
pQuiz09 = plot_vector_field((F[0]/n, F[1]/n), (x, -4, 4), (y, -4, 4), aspect_ratio = 1)
pQuiz09 += plot(-1*x, x, -4, 4, thickness = 2, color = 'red', xmin = -4, xmax = 4, ymin = -4, ymax = 4)
P1 = desolve_system_rk4(F, [x, y], ics=[0, 1, 1], ivar = t, end_points = [-5,5], step = 0.01)
S1 = [ [j, k] for i, j, k in P1]
pQuiz09 += line(S1, thickness = 2, axes_labels=['$x(t)$','$y(t)$'], xmin = -4, xmax = 4, ymin = -4, ymax = 4, color = 'blue')
show(pQuiz09)
pQuiz09.save('295_03-05_Quiz_09.pdf')