编写微分方程模块

differential_equation.py

@@ -0,0 +1,47 @@
+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()