Euler's Method for solving Differential Equations

eulers_method.py

def parse_location(s: str):
    if s.startswith("(") and s.endswith(")"):
        parts = s[1:-1].split(',')
        if len(parts) == 2:
            try:
                return tuple(map(int, parts))
            except ValueError:
                pass
    raise ValueError(f"Invalid location: {s!r}")

def eulers_method():
    equation_code = input("Differential Equation? ").strip()
    equation = compile(equation_code, '<equation>', 'eval')
    start = parse_location(input("Initial condition? "))
    step = float(input("Approximation step? "))
    end = float(input("Ending value of x? "))
    def run_equation(x, y):
        return eval(equation, globals(), {"x": x, "y": y})
    print()
    print(f"Approximating dy/dx = `{equation_code}` with initial condition {start} and step {step}")
    start_derivative = run_equation(*start)
    start_delta_y = start_derivative * step
    table = [(start, start_derivative, start_delta_y)]
    while abs(table[-1][0][0]) < abs(end):
        (x_old, y_old), derivative_old, delta_y_old = table[-1]
        updated_location = (x_old + step, y_old + delta_y_old)
        updated_derivative = run_equation(*updated_location)
        updated_delta_y = updated_derivative * step
        table.append((updated_location, updated_derivative, updated_delta_y))
    # Print a nice-markdown style table
    print("|   x   |    y    |   dy/dx   |   \u0394y   |")
    print("|-------|---------|-----------|--------|")
    for (x, y), derivative, delta_y in table:
        digits = 4
        x = round(x, digits)
        y = round(y, digits)
        derivative = round(derivative, digits)
        delta_y = round(delta_y, digits)
        print(f"|{x: < 7}|{y: < 9}|{derivative: < 11}|{delta_y: < 8}|")

if __name__ == "__main__":
    while True:
        eulers_method()
        if input("Do you want to continue [Y/n]?").lower() in ("no", "n"):
            break