Note that
and
You need to plug this information into your DE's, which are correct as far as they go. I'm assuming the units compatibility is taken care of by the constants and
Hi, I have the following problem and I am stuck in question 2. I would really appreciate it if you could check that the answer to question 1 is OK, and if you could also give me a hand with question 2.
"A tank of volume 2 , filled with water, is separated into two compartments and of identical volume by a semi-permeable membrane. Uranium is introduced into compartment at a constant mass rate . Uranium is exchanged between compartments and through the membrane at a rate given by , where and are the concentrations of Uranium in each compartment, and is a constant. Because Uranium is radioactive, its mass in each compartment also decays, at a rate proportional to mass, with proportionality constant .
Let and be the masses of Uranium in compartments and . Assume that there is no Uranium in the tank at , that is, , and that the water in each compartment is well mixed.
1.- Write down the differential equations for and describing their evolution.
2.- Find the masses at equilibrium."
So for the first one I have:
Is it correct? What about the second question, how do I work that out? Thanks!