$3$

$(25$ points$)$ The switch in the circuit below has been open for a long time. At $t=0,$ the switch flips. Determine $i(t)$ for $t>0$ and

$t{0}^{-}=10(\frac{10}{10+3+2})=6\mathrm{.}67$

$r$

$t{0}^{-}=t{0}^{+}$

$t_0^{+}=10(\frac{10}{10+5})=6\mathrm{.}67x$

$i(t)=0,t0$

$i(t)=[t{t}^{-}+t_0^{+}],e^{\frac{J}{t}}\frac{+}{{?}_0}x$