Update wronskian_second_order_de.py

Author: Venkat11Thadi

maths/wronskian_second_order_de.py

@@ -14,16 +14,15 @@
 References: https://tutorial.math.lamar.edu/classes/de/wronskian.aspx
 """
 
-import math
 import cmath
 
-
 def compute_characteristic_roots(
     a: float, b: float, c: float
 ) -> tuple[complex, complex]:
     """
     Compute characteristic roots for a second-order homogeneous linear DE.
-
+    a, b, c -> coefficients
+    
     >>> compute_characteristic_roots(1, -3, 2)
     (2.0, 1.0)
     >>> compute_characteristic_roots(1, 2, 5)
@@ -65,19 +64,27 @@ def classify_solution_type(root1: complex, root2: complex) -> str:
         return "Distinct Real Roots"
 
 
-def compute_wronskian(f, g, f_prime, g_prime, x: float) -> float:
+def compute_wronskian(
+    function_1: Callable[[float], float],
+    function_2: Callable[[float], float],
+    derivative_1: Callable[[float], float],
+    derivative_2: Callable[[float], float],
+    evaluation_point: float
+) -> float:
     """
-    Compute Wronskian determinant W(f, g) = f * g' - f' * g.
-
-    >>> import math
-    >>> def f(x): return math.exp(x)
-    >>> def g(x): return x * math.exp(x)
-    >>> def f_prime(x): return math.exp(x)
-    >>> def g_prime(x): return math.exp(x) + x * math.exp(x)
-    >>> round(compute_wronskian(f, g, f_prime, g_prime, 0), 3)
-    1.0
+    Compute the Wronskian of two functions at a given point.
+
+    Parameters:
+    function_1 (Callable[[float], float]): The first function f(x).
+    function_2 (Callable[[float], float]): The second function g(x).
+    derivative_1 (Callable[[float], float]): Derivative of the first function f'(x).
+    derivative_2 (Callable[[float], float]): Derivative of the second function g'(x).
+    evaluation_point (float): The point x at which to evaluate the Wronskian.
+
+    Returns:
+    float: Value of the Wronskian at the given point.
     """
-    return f(x) * g_prime(x) - f_prime(x) * g(x)
+    return function_1(evaluation_point) * derivative_2(evaluation_point) - function_2(evaluation_point) * derivative_1(evaluation_point)
 
 
 def construct_general_solution(root1: complex, root2: complex) -> str:
@@ -104,7 +111,8 @@ def construct_general_solution(root1: complex, root2: complex) -> str:
 def analyze_differential_equation(a: float, b: float, c: float) -> None:
     """
     Analyze the DE and print the roots, type, and general solution.
-
+    a, b, c -> coefficients
+    
     >>> analyze_differential_equation(1, -3, 2)  # doctest: +ELLIPSIS
     Characteristic Roots: (2.0, 1.0)
     Solution Type: Distinct Real Roots
@@ -142,3 +150,4 @@ def main() -> None:
 
 if __name__ == "__main__":
     main()  # doctest: +SKIP
+