Taking a Differential Equations Class; Can't remember/understand anything.

Hi,

I'm currently enrolled in a Differential Equations class at my local community college. I'm trying to get through the first problem, but I don't even remember/know what I'm doing.

Right now, I'm having trouble with classification by linearity. I can't tell (without guessing and looking at the back of the book (Giggle)) whether a DE is linear or non-linear.

An problem I'm having trouble understanding goes as:

Determine whether the given first-order DE is linear in the indicated dependent variable by matching it with the first differential equation given in (7)

$\displaystyle [(y^2)-1]dx + x dy = 0; in y; in x$.

The Answer Book said:

Writing the DE in the form x(dy/dx) = Y^2 = 1, we see that it is nonlinear in y because of y^2. However, writing it in the form of (y^2 - 1)(dx/dy) + x = 0, we see that it is linear in x.

I can't remember anything really about dx or dy and how the question got to the solution. If anyone can direct me to the subject online I should review (I have the 6e stewart book if anyone else knows/uses it).

I'm sorry for my ignorance; hope someone can help.