python第八章课后习题

8.4 求微分方程组的数值解 x'=-x^{3-y,x(0)=1,y'=x-y}3,y(0)=0.5,0<=t<=30，要求画出x（t）和y（t）的解曲线图形，再相平面上画出轨线

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import matplotlib.pyplot as plt
from scipy.integrate import solve_ivpdef system(t, state):x, y = statedxdt = -x**3 - ydydt = x - y**3return [dxdt, dydt]t_span = (0, 30)
y0 = [1, 0.5]sol = solve_ivp(system, t_span, y0, t_eval=np.linspace(t_span[0], t_span[1], 1000))x = sol.y[0]
y = sol.y[1]
t = sol.t# 绘制 x(t) vs t 和 y(t) vs t
plt.figure(figsize=(12, 6))plt.subplot(1, 2, 1)
plt.plot(t, x, label='x(t)')
plt.xlabel('t')
plt.ylabel('x(t)')
plt.title('x(t) vs t')
plt.legend()
plt.grid(True)plt.subplot(1, 2, 2)
plt.plot(t, y, label='y(t)')
plt.xlabel('t')
plt.ylabel('y(t)')
plt.title('y(t) vs t')
plt.legend()
plt.grid(True)plt.figure(figsize=(6, 6))
plt.plot(x, y, label='Phase Trajectory')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Phase Plane (x, y)')
plt.legend()
plt.grid(True)
plt.axis('equal')  plt.tight_layout()  
plt.show()print("学号：2023310143028")

8.5 求微分方程组(竖直加热板的自然对流)的数值解。(d^3f)/(dm3)+3f(d^f)/(dm2)-2((df)/(dm))^2+T=0,(d2T)/(dm^{2)+2.1f(dT)/(dm)=0，已知当m=0时,f=0,(df)/(dm)=0,(d}2f)/(dm^2)=0.68,T=1,(dT)/(dm)=-0.5。要求在[0,10]区间上，画出f(a)、T(a)的解曲线

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import matplotlib.pyplot as plt
from scipy.integrate import solve_ivpdef model(t, y):f, df_dm, d2f_dm2, T, dT_dm = yd3f_dm3 = -3 * f * d2f_dm2 + 2 * (df_dm)**2 - T  d2T_dm2 = -2.1 * f * dT_dm  # 注意通过 y 引用 freturn [df_dm, d2f_dm2, d3f_dm3, dT_dm, d2T_dm2]y0 = [0, 0, 0.68, 1, -0.5]t_span = (0, 10)
t_eval = np.linspace(t_span[0], t_span[1], 1000)sol = solve_ivp(model, t_span, y0, t_eval=t_eval, method='RK45')f = sol.y[0]
T = sol.y[3]plt.figure(figsize=(12, 6))plt.subplot(2, 1, 1)
plt.plot(sol.t, f, label='f(t)')  
plt.xlabel('t') 
plt.ylabel('f(t)')
plt.title('Solution for f(t)')
plt.grid(True)plt.subplot(2, 1, 2)
plt.plot(sol.t, T, label='T(t)', color='orange')  
plt.xlabel('t')  
plt.ylabel('T(t)')
plt.title('Solution for T(t)')
plt.grid(True)plt.tight_layout()
plt.show()print("学号：2023310143028")