college_computing_final_project/differential_equation.py

from sympy import *
from convert_formula import *

def solve_differential_equation(input):
    """
    求解微分方程
    """
    input = convert_formula(input)
    input = input.replace("''", ".diff(x,2)")
    input = input.replace("'", ".diff(x)")
    input = input.replace("y", "y(x)")
    x = symbols('x')
    y = symbols('y', cls=Function)
    l = input.split('=')
    diffeq = Eq(sympify(l[0]), sympify(l[1]))
    result = dsolve(diffeq, y(x))
    return result

def test_differential_equation():
    """
    测试求解微分方程的函数
    """
    input = "y''+2y'+3y=0"
    result = solve_differential_equation(input)
    assert str(result) == 'Eq(y(x), (C1*sin(sqrt(2)*x) + C2*cos(sqrt(2)*x))*exp(-x))'
    input = "y'-2y=3"
    result = solve_differential_equation(input)
    assert str(result) == 'Eq(y(x), C1*exp(2*x) - 3/2)'
    input = "y'+2y=3"
    result = solve_differential_equation(input)
    assert str(result) == 'Eq(y(x), C1*exp(-2*x) + 3/2)'

def UI():
    """
    微分方程求解器的用户界面
    """
    while True:
        inputs = input("请输入微分方程（输入q退出）：（只支持自变量为x，因变量为y）")
        if inputs == "q":
            break
        result = solve_differential_equation(inputs)
        print("解为：")
        pprint(result)

if __name__ == "__main__":
    test_differential_equation()
    UI()