一阶微分方程

$$\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}+x=\mathrm{s}\mathrm{i}\mathrm{n}\left(t\right)$$

from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt


def func(y, t):
    x = y
    dx = -x+np.sin(t)
    return dx


t = np.arange(0, 10, 0.001)
sol1 = odeint(func, [0], t)
fig = plt.figure(figsize=(16,8))
plt.plot(t, sol1[:,0], label='x')
plt.legend(fontsize=15)
plt.show()

二阶微分方程

以下面的方程为例
$$\frac{d^{2}x}{{\mathrm{d}\mathrm{t}}^2}+\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}+x=\mathrm{s}\mathrm{i}\mathrm{n}\left(t\right)$$

from scipy.integrate import odeint
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt


def func(y, t):
    x, dx = y
    d2x = [dx, -dx-x+np.sin(t)]
    return d2x


t = np.arange(0, 10, 0.001)
sol1 = odeint(func, [0, 0], t)
fig = plt.figure(figsize=(16,8))
plt.plot(t, sol1[:,0])
plt.plot(t, sol1[:,1])
plt.show()

sol1 = odeint(func, [0, 0], t)中[0, 0]是传递给func函数的初始值，func是待解的方程。

二阶微分方程组

$$\frac{d^{2}x}{{\mathrm{d}\mathrm{t}}^2}+y\frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}+x=\mathrm{s}\mathrm{i}\mathrm{n}\left(t\right)$$
$$\frac{d^{2}y}{{\mathrm{d}\mathrm{t}}^2}+x\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{t}}+y=1$$

from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt


def func(y, t):
    x, dx, z, dz = y
    d2q = [dx, -z*dx-x+np.sin(t), dz, -x*dz-z+1]
    return d2q


t = np.arange(0, 10, 0.001)
sol1 = odeint(func, [0, 0, 0, 0], t)

fig = plt.figure(figsize=(16,8))
plt.plot(t, sol1[:,0], label='x')
plt.plot(t, sol1[:,2], label='y')
plt.legend(fontsize=15)
plt.show()

sol1里对应着x，dx/dt，y，dy/dt