I've worked this problem several times. I know I am making some sign errors along the way but I don't think that can account for the difference between my solution and the one in my text book.
I obtained solutions to homogeneous equation ; and so the Wronskian is
the particular solution takes the form where and where the driving force
so,
and
and so
and finally the general solution
but the solution in my text book is
and I can't figure out where the sin term was supposed to disappear.
Any pointers will be very appreciated.
That worked out so much easier than what I was trying to do. Thank you very much. The terms of v are actually both negative but I noticed that when I worked through it again using the substitution.
*sigh* I stink at integration, I need to be able to see alternative options better when my first attempts don't work so great.