$3.$ Consider the circuit shown below.

$($a$)$ Derive a current$-$voltage state space representation for the circuit. Assume the output $\backslash ($ y$($t$)\backslash )$ is measured as the voltage across the capacitor.

$($b$)$ Find the transfer function, $\backslash ($ H$($s$)\backslash ),$ of the system from the state space representation found in part $($a$).$