Final answer:
The existence/uniqueness theorem cannot be applied to the equation y² - 1 to guarantee a solution, as the equation does not fit the required form dy/dx = f(x, y), and crucial information is missing.
Step-by-step explanation:
The existence/uniqueness theorem concerns ordinary differential equations and states that if a function f(x, y) and its partial derivative ∂f/∂y are both continuous in a region around a point (x0, y0), then there is a unique solution y(x) to the differential equation dy/dx = f(x, y) that passes through the point (x0, y0). However, the differential equation given in the question, y² - 1, does not fit the form dy/dx = f(x, y), rather it seems to be an implicit form of a potential differential equation, but as written, it is not clear. Therefore, based on the incomplete information provided in the question, the existence/uniqueness theorem cannot be applied to guarantee a solution through a given point.