The switch in Figure P9=37. has been closed for a long time and is opened at \(t=0\). The circuit parameters are \(R=\) \(22 \mathrm{k} \Omega, L=220 \mathrm{mH}\), and \(V_{\mathrm{A}}=10 \mathrm{~V}\).

(a) Find the differential equation for the inductor current \(i\) \(\mathrm{L}(t)\) and initial condition \(i_{\mathrm{L}}(\mathrm{o})\).

(b) Transform the equation into the \(s\) domain.

(c) Solve the equation for \(I_{\mathrm{L}}(s)\).

(d) Take the inverse transform of \(I_{\mathrm{L}}(s)\) to find \(i_{\mathrm{L}}(t)\).

(e) Validate your result using Multisim.