11"""
22wronskian_second_order_de.py
3- A symbolic and numerical exploration of the Wronskian
3+ A symbolic and numerical exploration of the Wronskian
44for second-order linear differential equations.
55
66This program:
@@ -68,12 +68,13 @@ def classify_solution_type(root1: complex, root2: complex) -> str:
6868
6969from typing import Callable
7070
71+
7172def compute_wronskian (
7273 function_1 : Callable [[float ], float ],
7374 function_2 : Callable [[float ], float ],
7475 derivative_1 : Callable [[float ], float ],
7576 derivative_2 : Callable [[float ], float ],
76- evaluation_point : float
77+ evaluation_point : float ,
7778) -> float :
7879 """
7980 Compute the Wronskian of two functions at a given point.
@@ -88,8 +89,9 @@ def compute_wronskian(
8889 Returns:
8990 float: Value of the Wronskian at the given point.
9091 """
91- return function_1 (evaluation_point ) * derivative_2 (evaluation_point ) - \
92- function_2 (evaluation_point ) * derivative_1 (evaluation_point )
92+ return function_1 (evaluation_point ) * derivative_2 (evaluation_point ) - function_2 (
93+ evaluation_point
94+ ) * derivative_1 (evaluation_point )
9395
9496
9597def construct_general_solution (root1 : complex , root2 : complex ) -> str :
@@ -155,4 +157,3 @@ def main() -> None:
155157
156158if __name__ == "__main__" :
157159 main () # doctest: +SKIP
158-
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