Find the solution of the differential equation
\(\frac{\mathrm{d}^{2} x}{\mathrm{~d} t^{2}}+6 \frac{\mathrm{~d} x}{\mathrm{~d} t}+9 x=18 t^{2}+6 t+1\)
given that, when \(t=0, x=3\) and \(\frac{\mathrm{d} x}{\mathrm{~d} t}=0\).