, where x does not equal zero

I was to find the particular solution of this equation with the initial condition f(-1) = 1. I did so and found y = -1 (hopefully this is correct!)

However, I'm also asked to give the domain of this solution. I'm really confused about when you should and shouldn't restrict domain (when to have absolute value signs on ln, for example), so I don't know how to answer this.

Help, please?