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.