In pharmaceutical studies it is important to model and track concentrations of chemicals int he blood and in the blood tissues. Let x and y denote the amounts of a certain drug in the blood and in the tissues, respectively. Assume that the drug in the blood is taken up by the tissues at a rate r1x and is returned to the blood from the tissues at a rate r2y. At the same time the drug amount in the blood is continuously degraded by the liver at the rate r3x. note r1 r2 r3 >0
Write down the model equations, find the e-values of the matruc and determine the response of the system to an intial dose of x(0) = x0 given intravenously, with y(0) = 0
What I want to know is whether:
dy/dt = r1x - r2y
dx/dt = (-r1-r3)x + r2y
Because when I use these equations to form the matrix A it gives a really messy matrix and close to impossible to find the eigenvectors