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Example:

[itex]\textit{y' = }\frac{(x - 1)}{y}[/itex]

With this equation I can see that as long as [itex]\textit{y ≠ 0}[/itex] a solution exists.

But now if I'm asked to find a given interval where a solution exists and is unique, I'm confused :P What should I be looking for in the equation/direction field?

Here's the direction field for that differential equation: