The switch in Figure P9=43 has been open for a long time and is closed at \(t=0\).

(a) Find the circuit differential equation in \(i_{\mathrm{L}}(t)\) and the initial conditions \(i_{\mathrm{L}}(\mathrm{O})\) and \(v_{\mathrm{C}}(\mathrm{o})\).

(b) The circuit parameters are \(L=10 \mathrm{H}, C=1.25 \mu \mathrm{F}, R_{1}\) \(=10 \mathrm{k} \Omega, R_{2}=3.3 \Omega\), and \(v_{\mathrm{S}}=10 u(t) \mathrm{V}\). Use Laplace transforms and MATLAB to solve for \(i_{\mathrm{L}}(t)\) for \(t \geq 0\).

(c) Simulate the circuit in Multisim to plot your resulting waveform.