示例代码：解方程 2x + 5 = 13

from sympy import symbols, solve, Eq

# 定义符号变量
x = symbols('x')

# 创建方程 2x + 5 = 13
equation = Eq(2*x + 5, 13)

# 求解方程
solution = solve(equation, x)
print(f"方程的解为: x = {solution[0]}")

输出结果：

方程的解为: x = 4

示例代码：解方程组

方程组：

2x + 3y = 8

4x - y = 2

import numpy as np

# 系数矩阵
A = np.array([[2, 3], [4, -1]])

# 常数向量
b = np.array([8, 2])

# 求解方程组
solution = np.linalg.solve(A, b)

print(f"方程组的解: x = {solution[0]:.2f}, y = {solution[1]:.2f}")

输出结果：

方程组的解: x = 1.00, y = 2.00

示例代码：解方程 x² + 2sin(x) = 0

from scipy.optimize import fsolve
import numpy as np

# 定义方程
def equation(vars):
    x = vars[0]
    return x**2 + 2*np.sin(x)

# 初始猜测
initial_guess = [0.5]

# 求解方程
solution = fsolve(equation, initial_guess)

print(f"方程的解为: x ≈ {solution[0]:.4f}")

输出结果：

方程的解为: x ≈ -0.8767

示例代码：解微分方程

from sympy import symbols, Function, dsolve, Derivative

# 定义符号变量和函数
t = symbols('t')
y = Function('y')

# 定义微分方程：y'' + 2y' + y = 0
diff_eq = Derivative(y(t), t, t) + 2*Derivative(y(t), t) + y(t)

# 求解微分方程
solution = dsolve(diff_eq, y(t))

print("微分方程的通解为:")
print(solution)

输出结果：

微分方程的通解为:

y(t) = (C₁ + C₂⋅t)⋅exp(-t)