Problem $2.$ The ZSR transfer function between a circuit's input $v_1(t)$ and its output $v_2(t)$ is

$H(s)=\frac{V_2(s)}{V_1(s)}=\frac{10s+1000}{s+1000}$

$($a$)$ What is the circuir's input$-$output differential equation?

$($b$)$ What is the circuit's unit step response?

$H(s)=\frac{V_z(s)}{V_z(s)}=\frac{10x+1000}{s+1000}$

c$.$ What is the circuits output when the input is v$1($t$)=$ e$^-100$t V

$($d$)$ Design a circuit using realistic component values that implements the transfer function.