Solving u double-prime plus u-prime plus u equals one

Find the general solution of the differential equation $u''(t)+u'(t)+u(t)=1$.

$u(t)=1+e^{-t/2}\left(A\cos\tfrac{\sqrt3}{2}t+B\sin\tfrac{\sqrt3}{2}t\right)$. The constant $u=1$ is a particular solution. The characteristic equation $r^2+r+1=0$ has roots $-\tfrac12\pm\tfrac{\sqrt3}{2}i$, giving the damped oscillatory homogeneous part.