SOLVED... You can ignore this ;D

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

$\displaystyle y' + y*tan(x)=sin(2x)$,$\displaystyle y(0)=1$

I use the integrating factor $\displaystyle |sec(x)|$ and get the solution

$\displaystyle y=k*|cos(x)|-2*cos^2 (x)$

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 $\displaystyle u=e^{\int tan(x) dx}$

Thanks