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Determine whether the given first order differential equation is linear in the following variables:

$(y^2-1)dx+xdy=0$; in x and y

I'm pretty confused here. I've seen $\frac{dy}{dx}$ but what do $dy$ and $dx$ mean when they're separated? Anyways, I rewrote the equation to something I recognize better $x\frac{dy}{dx}=-y^2+1$. The answer key has linear in x but not in y. Is the reason it is not linear in $y$ because $y$ is squared? Does it make sense to say it is linear in x because x doesn't even have any derivatives? For example would you say $y'+x=y$ is linear in x and y?

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This equation is linear in $x$. But it is not linear in $y$ because $y$ has power $2$ in the equation.

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