(Solved): a. For the circuit below, find the differential equation for \( \mathrm{v}_{\mathrm{t}}(\mathrm{t} ...

a. For the circuit below, find the differential equation for \( \mathrm{v}_{\mathrm{t}}(\mathrm{t}) \) as a function of \( \mathrm{v}_{\mathrm{s}}(\mathrm{t}) \) when \( i_{s}(t)=0 \). Make sure the coefficient in front of the highest order derivative term is unity. \( b \). For the circuit below, find the differential equation for \( v_{t}(t) \) as a function of \( i_{s}(t) \), when \( \mathrm{v}_{\mathrm{s}}(\mathrm{t})=0 \). Make sure the coefficient in front of the highest order derivative term is unity.