Consider a first-order system with a forcing function \(f(t)\) such that input-output differential equation is given by

\[\begin{equation*}\dot{y}+3 y=f(t) \text {, } \tag{3.7}\end{equation*}\]

where \(y(0)=1\). Find the dynamic system response \(y(t)\) for the following forcing functions:

(a) \(f(t)=5\)

(b) \(f(t)=5 \cos 2 t\).