Find the particular solution y=f(x) to dy/dx=(1+y)/x given that f(-1)=1 and state its domain.(adsbygoogle = window.adsbygoogle || []).push({});

My answer was: 2|x|-1, x ∈ ℝ/{0}

Apparently, the domain should be x<0

Solving the differential equation was not an issue at all, but I have no idea why the domain is restricted to x<0. I understand that zero cannot be included because dy/dx fails to exist at x=0, but why are positive real numbers not included?

In general, as well, how is the domain of a particular differential equation found that is not obvious (e.g. found by simply looking at dy/dx)

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# Domain of a Differential Equation

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