First off, I read the sticky, I hope to understand it all one day (Giggle)

I am supposed to verify the the solution of the differential equation:

Solution: -cosx ln abs(secx + tan x). The equation is y" +y = tanx

Now, I have the solution spelled out in my answer guide, but I don't know how they got from step to step (just so you know I'm not looking for an answer handout)