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- [Lecturer] Welcome to a second lesson on mixture problems involving first order differential equations. In this video, well focus on different inflow and outflow rates. So if we let A of T be the amount of substance dissolved in the liquid of a tank at any time T, where liquid is entering and leaving the tank, and the liquid entering the tank will have a different concentration of the substance dissolved in it. So if this is the case, we can model the change of the mixture using the differential equation DA/DT equals R sub one minus R sub two where DA/DT is a rate at which A of T is changing in the tank, R sub one is a rate at which A of T is entering the tank and R sub two is a rate at which A of T is leaving the tank. To get a visual of this We have a certain concentration being pumped into our mixing tank and then pumped out. And for our example, the inflow rate and outflow rate will be different and because theyre different, notice how the inflow rate is going to be higher