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Differential Equationsmedium
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Which condition on the function f(x,y)f(x,y)f(x,y) guarantees the existence of a unique solution to the initial value problem dydx=f(x,y)\frac{dy}{dx} = f(x,y)dxdy​=f(x,y) with y(x0)=y0y(x_0) = y_0y(x0​)=y0​ in a neighborhood of (x0,y0)(x_0, y_0)(x0​,y0​)?