a$)$ An engineer disconnects the DC input to an electrical circuit. As such, the potential difference $v(t)$ at the output starts to change $(v$ in volts, $t$ in milliseconds$).$ Furthermore, this potential difference turns out to be governed by the following ODE:

$\frac{1}{5}{v}^{}+2v^{}+5v=0$

with initial conditions $v(0)=6$ and $v^{}(0)=0.$

Use any method taught in this module to find the particular solution of this ODE $\text{'}$by hand'; and

solve the ODE using Laplace method and give correct final answer