A recirculatory pharmacokinetic model[1]of an anesthetic drug delivered intravenously is shown below. The model incorporates physiological processes that are important determinants of intravenous anesthetic disposition including cardiac output, lung kinetics, and injection rate of intravenous bolus administration of the drug. The two compartments represent the lungs and body with respective distribution volumes, V_Land V_B. Q_COis cardiac output, or rate of circulation of blood (L/min) between the two compartments.C_vrepresents drug concentrations (mg/L) in the venous circulation upstream of the drug infusion site and returning from the body to the lungs.C_arepresents drug concentrations (mg/L) in the arterial circulation emerging from the lungs and entering the rest of the body.Q_Clis the clearance rate, or rate of removal of the drug (L/min).R₀is the drug infusion rate (mg/min).During bolus injection, infusion can be treated as dose (D, mg) given over a time interval equal to the duration of the injection (t_D) and expressed as R₀= D / t_D(mg/min). After bolus injection, the infusion rate is zero (R₀= 0). The system of differential equations for the model are derived by mass balance of the rates that drug enters and leaves the compartments

A) Find general solutions for the system of ordinary differential equations (ODEs) given in the problem statement analytically (by hand) for the homogeneous case (after infusion).You do not need to apply initial conditions.

Recirculatory Model Model Equations VL Lung Qco Ro VL . dt dCa - Ro - Qco . (Ca - Cv) Ca VB . dt dev = Oco . (Ca - Cv) - Qci - Ca Qco Body Qc VB During Infusion After Infusion D = 100 mg, to = 0.5 min Ro = 0 mg/min Ro = P (mglmin) Ca (0) = 24 mg/L Ca (0) = 0 mg/L Cy (0) = 1.8 mg/L Cv (0) = 0mg/L VL = 2.5L VL = 2.5L VB = 15 L VB = 15 L eco = 6 Llmin eco = 6 Limin Qci = 2 Llmin 2ci = 2 Llmin