A certain LTIC system is described by the following differential equation

\[
\frac{d^{2} y(t)}{d t^{2}}-\frac{d y(t)}{d t}-30 y(t)=\frac{d x(t)}{d t}+4 x(t)
\]

The system is subjected to the following input.

\[
x(t)=e^{-3 t} u(t)
\]

The initial conditions are \(y\left(0^{+}ight)=3\) and \(\dot{y}\left(0^{+}ight)=1\). Derive an expression for the output response as a function of time.