dy/dx= (y^2 -1)/x

1. Give the general equation of the curves that satisfy this equation.

2. Show that the straight lines y=1 and y=-1 are also solutions

3. Do any of the curves you found in 1) intersect y=1?

My Ans:
1. The general solution i found out to be x^2 + C = (y-1)/(y+1), correct?

2. Does that mean y=1 is a solution and y=-1 is not because it will have a denominator of zero?

3. The only intersection is at x=0, y=1 , since x can't be 0, there are no curves intersecting y=1

Am i doing anything wrong here?