Please use Matlab to solve this problem, thanks.

Project 6.2 Figuure P6.2a shows a third order RIcircuit. To run a timc domain tansicnt amal ysis, we transform the circuit into differential equations using the following method: C1 C2 2 ci C2 C1 Ne Vs Figure P6.2a Third-order RLCC circuit containing two capacitors and an inductor. First, write Kirchhoff's current law for each node in the circuit: at node 1: ici + ic2-i-0 (P6.2a) at node 2: iR + ic20 (P6.2b) Second, write Kirchhoff's voltage law for the two loops in the circuit: for loop 1: vs - vci- v for loop 2: vI + vC2-UR 0 (P6.2c) 0 (P6.2d) Third, write the constituent relations for each circuit element: (P6.2e) (P6.2f) (P6.2g) (P6.2h) for Cl: k1 GUCI for L: UL = LL for R: vR-IRR We choose the three voltages and currents with derivative terms (vci, Vc, and i as the state variables for this problem 1. Rearrange equations (P6.2a)-(P6.2h) into the following standard form: dvc (P6.2i) = J (UCI,UC 2 , IL,US(t)) dt dvc2 dt (P6.2j) di dt (P6.2k) where the functions f gand hinvolve parameters C, C2, L, and R. vst) 5 V t (usec) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Figure P6.2b Input pulse for the RLCC circuit. 2. Solve Equations (P6.2i)-(P6.2k) with the Runge-Kutta algorithm for the fol- lowing circuit parameters: G-1 F, C2-0.001 F, R-100 kQ, L-0.01 mH. Use a time interval of 0 ts 105 and a step size of 0.01 s. Assume v(t) is a 5-V pulse starting at time t-0 with rise time of 0.1 s, an "on" time of 0.8 us, and fall time of 0.1 us (as shown in Figure P6.2b). Initial conditions: VCI (0)-0, VC2 (0)-0 , and i1 (0)-0 . 3. Plot on separate graphs: vci(t), vc2(t), in(t) and vs(t) versus time