Ononot — Which condition on the function f(x,y) guarantees the existe

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Differential Equationsmedium

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Which condition on the function $f(x,y)$ guarantees the existence of a unique solution to the initial value problem $\frac{dy}{dx} = f(x,y)$ with $y(x_0) = y_0$ in a neighborhood of $(x_0, y_0)$ ?