I'm trying to find the particular solution $y_p$ for:
I set $y_p(x)=A\sin x + B\cos x$ and differentiate 2 times: $$y_p'(x)=A\cos x - B\sin x$$ $$y_p''(x)=-A\sin x - B\cos x$$ I Insert into $$y_p''+y_p=\sin x$$
$$-A\sin x - B\cos x+ A\sin x + B\cos x=\sin x$$
And this cant be right, because the LHS. is $=0$
Where did I go wrong?