6. (Optional) The circuit shown is linear and time-invariant. a. Write the differential equation with vc as the dependent variable, and indicate theproper initial conditions as functions of vc(0), and

i¿(0). Hint: Write a KCL atnode 1, expressing i, in terms of vc and its derivative, and then a KVL in termsvc as an independent variable. b. Calculate the zero-input response vc(t), and i¿(t). Assume i¿ (0) = 1A, and%3D v_{c}(0)=4 V . R_{1}=4 \Omega, R_{1}=2 \Omega, L=1 H, \text { and } C=\frac{1}{2} F