For the inverting OP AMP circuit shown in Figure P9-4.7., write a differential equation for \(v_{\mathrm{O}}(t)\) in terms of the elements and \(v_{\mathrm{S}}(t)\). Assume \(v_{\mathrm{C}}(0)=0\). Then let \(v_{\mathrm{S}}(t)=e^{-10}\)\({ }^{t} u(t) \mathrm{V}, R_{1}=1 \mathrm{k} \Omega, R_{2}=10 \mathrm{k} \Omega\), and \(C=1 \mu \mathrm{F}\) and using Laplace techniques, find the output \(v_{\mathrm{O}}(t)\).