SOLVED... You can ignore this ;D

When I solve the following First-Order Linear ODE I get the wrong answer....

,

I use the integrating factor and get the solution

While a textbook and wolfram alpha say that there should be no absolute value sign around the cos(x)....

I think my problem was in determining the integrating factor, can anyone explain what I did wrong? I used the formula [LaTeX ERROR: Convert failed]

Thanks