2. Modeling and Solving
(1) Find the current $I(t)$ of the RL-series circuit with $E(t) = 100V$, $R = 10\Omega$, $L = 2H$, and that
the current is initially zero.
(2) Find the current $I(t)$ of the RC-series circuit with $E(t) = 100V$,
$R = \begin{cases} 200 - t, & 0 \le t \le 200 \\ 10, & t > 200 \end{cases} \Omega$,
and $C = 0.25F$.
(3) The tank in Figure contains 200 lb of salt dissolved in 1,000 gal of water. The inflow per
minute is $1 + \cos t$ lb of salt dissolved in 50 gal of water. The outflow is 50 gal min of the
uniform mixture. Find the salt $y(t)$ in the tank.