Problem $2(50$pts$)$: For the RLC parallel circuit shown below, determine the followings:

a$)$ the second$-$order equation for voltage $v$

b$)$ the characteristic equation for the circuit

c$)$ the roots and type of natural response

d$)$ the complete response for voltage v

I. C $i(0)=-4$A and $v(0)=10V$ Given: $R=1,C=2F,L=10H,i_S=5e^{-3t}u(t)A$