I can't really show the slope field, but I don't believe the image is needed for this problem. But either way, the slopes end up looking something like this:

In other words, a hyperbola.

I have two questions concerning this:

1) Consider the differential equation

, where y (does not equal) 0. (sorry, I don't know the latex/symbol for that)

Find the particular solution y=f(x) to the differential equation with the initial condition f(3) = -1, and state its domain.

I tried to solve it, but got y=x, which I am sure is wrong. What am I doing wrong?

b) I didn't really learn slope fields too well either. Is the image that's shown through the slope fields the original function or the graph of the derivative?

Thank you in advance once again!