# Solve this differential equation?

Posted 10 months ago
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 I'm trying to use Mathematica to try and solve differential equations to model the process described in the figure. However, I'm having some trouble forming the correct differential equations to describe the process. The states are the subscripted capital letters, (e.g. Mr, Nn,n, etc). My process is weird because it combines processes governed by first-order rates, the lambdas, with processes governed by constant time, the taus. For example, Nnn is formed by two first order rates, but it decays into Ncn through a time constant process where one Nnn takes taus time to become Ncn. Truly, I only need an equations for the sum two of the states, Nc,n and Nc,c, as a function of time. The problem emerges for the differential equation for Ncn. When solved, it will become negative at time tauT when lambdan is very small (compared to lambdab). That should be impossible in the process, so clearly I'm modeling this wrong. Any help with formulating the correct differential equation would be very helpful. Or if there is another approach I should take, please let me know. Thank you.