$7\mathrm{.}88$ The voltage v$1($t$)$ in a network is defined by the equation $2$

d v$1($t$)+2$ c dv$1($t$)$ d $+5$v $($t$)=0$

Find

$($a$)$ the characteristic equation of the network. $($b$)$ the circuit$$s natural frequencies.

$($c$)$ the expression for v$1($t$).$