Find a particular solution of $\displaystyle y^{(3)}+y'=2-sinx$

Solution:

The homogeneous solution is $\displaystyle y_h(x)=C_1+C_2 \cos x + C_3 \sin x $

Now, my first guess for the particular solution is: $\displaystyle y_p(x)=A+B \sin x+C \cos x $

I have all terms repeated here, so multiply by x to all, obtains:

$\displaystyle y_p(x)=Ax+B x \sin x + C x \cos x $

Would that be the right guess? Somehow the answer that I obtain from this doesn't match with the one in the book.

Thanks.