Just had a few questions that are on my mind about knowing how to tell one form from the other. The forms that we have learned are

1. Separable (Easiest)

2. Linear

3. Exact

4. Bernoulli

5. Homogeneous

Questions:

1. I know that Linear is of the form

dy/dx + P(x)y = Q(x). Given that y is the dependent variable, for this to work Q(x) cannot have any y variable correct? IF Q(x) DID have a y variable to the nth power, then it would be Bernoulli right?

2. For a D.E. to be considered Exact, it must first pass the test for exactness even though it is of the form P(x)dx + Q(x)dy = 0 correct?

3. I'm having a hard time knowing initially which method will prove to be the fastest and most efficient given some random problem in the book. Any tips or tricks you guys can let me know about?

So far that's all the questions I have. Any feedback is much appreciated.