I will say what Krizalid said, but in a more general way.
For a differential equation of the form:
we define as the integrating factor of the differential equation. We solve the differential equation by multiplying through by the integrating factor. so we get the new equation:
it will always be the case that the left hand side is the derivative we would get from applying the product rule. so the equation becomes:
is our solution
remember that you will get an arbitrary constant from the integration, you have to divide this by as well
yes, that is fine, and incidentally, that is exactly the process i described to you above. i tried to save you the trouble of trying to get it from you text book, sometimes those things are ... let's just say, I hate the text that i used for differential equations. the only thing i like about it is that it gives the answers for even as well as odd problems, which is rare for textbooks to do