2. Modeling with differential equations:

a. Write the differential equation that relates the current through the

capacitor to the voltage across the capacitor. Substitute for the state

variables x₂ (t) and x₂ (t) according to question 1.

Complete as appropriate,

x₁ (t) =

x₂ (t) =

b. Write the differential equation that relates the current through the

inductor to the voltage across the inductor. Derive the 2nd differential

equation by applying KVL around the circuit. Substitute for the state

variables x₁ (t) and x₂ (t) according to question 1.

Complete as appropriate,

x₁ (t) =

x₂ (t) =