Consider a system that has the input-output differential equation (Input-Output model)

\[a_{1} y+a_{2} \dot{y}+a_{3} \ddot{y}=b_{1} u+b_{2} \dot{u},\]

where the input is \(u(t)\) and output is \(y(t)\) where all initial conditions are zero. Find the system response \(y(t)\).