(Solved): (1) Find a differential equation that describes the behavior of the circuit. (2) What is the range ...

(1) Find a differential equation that describes the behavior of the circuit. (2) What is the range of possible decay (when output has decayed to less than $1\%$ of the maximum transient value) in seconds? (3) Calculate the current $\mathbf{i}(\mathbf{t})$ in this circuit for $\mathbf{t}?0$. Assume the following initial conditions: $i_L\left(0^{?}\right)=1[A],v_C\left(0^{?}\right)=10[\mathrm{V}]$