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So today is was my first day of differential equations and I understood most of it until the very end. My professor started talking about partial derivatives which is Calc 3 at my university. He said Calc 3 wasn't required but was recommend for differential equations. He then went on to act like we all knew Calc 3.

So he gave us this homework question:

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through point (x_0, y_0) in the region(x_0 is x sub 0):

x(dy/dx) = y

I pretty much have no idea how to solve this or really what it's asking. The rest of the homework was really easy so this caught me off guard.

The only information we learned about it is the attachment I uploaded.

Do I need to define a region(IE a box) or is it just an interval. If it's an interval, I think I can answer it. But I seriously don't even understand what the theorem is saying. Is it saying that given a family of differential equations (for example x + C ) and given a point, there is only one C that will cause the function to intersect that point? I don't think that's it because it doesn't involve a region. I think I don't understand it because I have no idea what a partial derivative is.

Any help would be appreciated.

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# Uniqueness Theorem: Finding region

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