(a) The differential equation
\frac{d^{2} y}{d t^{2}}+6 \frac{d y}{d t}+9 y=\cos t
has initial conditions, y(0)=1, y^{\prime}(0)=2. Find Y(s) and, without finding y(t), determine what functions of time will appear in the solution.
(b) If Y(s)=\frac{s+1}{s\left(s^{2}+4 s+8\right)}, find y(t).