DSolve[{Derivative[1][x][t] == (k (-x[t] + y[t]))/Subscript[V, A], Derivative[1][y][t] == (k (x[t] - y[t]))/Subscript[V, B], x[0] == Subscript[x, 0], y[0] == Subscript[y, 0]}, {x[t], y[t]}, {t, 0, 200}]
Given :dx/dt
=k/Subscript[V, A] (y-x) dy/dt
=k/Subscript[V, B] (x-y)
where Subscript[V, A] and Subscript[V, B] are the volumes of the compartments and k > 0 is a permeability factor. Let x(0) = Subscript[x, 0] and y(0) = Subscript[y, 0] denote the initial conditions for the nutrient. Solely on the basis of equations in the system and the assumptions Subscript[x, 0] > Subscript[y, 0] > 0, sketch on the same set of coordinate axes possible solution curves of the system. Explain your reasoning. Discuss the behavior of the solutions over a long period of time. I want to know if i typed something wrong or if the problem is wrong