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Hello Everyone.

I have a question. Suppose I have a differential equation for which I want to find the values at which [itex]\displaystyle f(x,y)[/itex] and [itex]\displaystyle \frac{\partial f}{\partial y}[/itex] are discontinuous, that I might know the points at which more than one solution exists. Suppose that [itex]\displaystyle y_1[/itex] is such a value. Now suppose we want to find a unique solution at [itex]\displaystyle (x_0, y_0)[/itex], and that it exists. My question is, can the region that encloses [itex]\displaystyle (x_0,y_0)[/itex] also include [itex]\displaystyle y_1[/itex]?

I have a question. Suppose I have a differential equation for which I want to find the values at which [itex]\displaystyle f(x,y)[/itex] and [itex]\displaystyle \frac{\partial f}{\partial y}[/itex] are discontinuous, that I might know the points at which more than one solution exists. Suppose that [itex]\displaystyle y_1[/itex] is such a value. Now suppose we want to find a unique solution at [itex]\displaystyle (x_0, y_0)[/itex], and that it exists. My question is, can the region that encloses [itex]\displaystyle (x_0,y_0)[/itex] also include [itex]\displaystyle y_1[/itex]?

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