Hey folks!

Long time since I posted here!

I would just like to run by you a differential equation that models the mass flow in a Completely mixed reactor under step input that I have solved, but my lecture notes present a different solution.

$\displaystyle V \frac{dc_e}{dt} = Qc_i-Qc_e-kVc_e$

V, c_i , Q and k are constants.

$\displaystyle V \cdot \int_c_i^{c_e}\frac{1}{Qc_i-c_e(Q+kV)} dc_e = \int_0^t dt$

I came up with the final answer of :

$\displaystyle c_e = \frac{QC+ kVc_ie^{-\frac{Q+kV}{V} \cdot t}}{Q+kV}$

My lecture notes present a final solution of:

$\displaystyle c_e = \frac{Qc_i - Qc_i e^{- \frac{kV+Q}{V} \cdot t} }{Q+kV} $

If some one could shed some light on this, I would really appreciate it!

Thank you.