Consider the RLC circuit shown below, where the inital current flowing through the circuit at time t = 0 is Io = 5, and the initial charge on the capacitor at time t = 0) is Qo = 2. The components have values of R = 100 , L = 5 H, and C= 1 450, 500 F. (v(t)) R C I a) Write a differential equation for Q(1), the charge across the capacitor, assuming the voltage source V(t) = 0. b) Classify the differential equation c) Identify an appropriate solution technique, and solve the differential equation for Q(t). d) Use MATLAB to plot your solution for time t = 0 to 1. Solution: e) Use the MATLAB dsolve() function to solve the differential equation and plot the solution on a new figure. The results provided by dsolve() and your solution from part (b) should match.