Forced ODE y'' + y' + y with constant and linear right sides

Find the general solutions of (a) $y''+y'+y=1$ and (b) $y''+y'+y=x$.

(a) $y=1+y_h$; (b) $y=x-1+y_h$, where $y_h=e^{-x/2}\left(c_1\cos\tfrac{\sqrt3}{2}x+c_2\sin\tfrac{\sqrt3}{2}x\right)$. Try a polynomial of the same degree as the forcing: $y=A$ gives $A=1$; $y=Ax+B$ gives $A=1$ and $A+B=0$.