Why not separable (basic question)?

[jla2w]

In Example 1.5 of Differential Equations Demystified, the equation is y' +2xy = x, and the author claims this is not separable. Now, what am I missing. I try the following.

1) dy/dx = x - 2xy
2) dy/dx = x(1-2y)
3) dy/(1-2y) = xdx

I guess one of those is invalid but I just cannot identify which. Any help appreciated, thanks. This is part of an effort to brush up on ODE since it's been years since I took it and now I'm going for a Master's in Applied Math, need lots of help of this kind. Thanks

[Pengwuino]

Hmm, are you sure that's the equation they gave? I don't see what's wrong with that.

[jla2w]

Yes, that's definitely the equation, and the author says
"This equation is plainly not separable (try and convince yourself that this is so)."

[arildno]

Maybe it isn't separable but I don't see how it's "plainly" not separable, you seem to agree
You just separated it, disproving the author's claim.

[jla2w]

Author wrote me back saying that it was a mistake, so that is in fact a separable equation.