KFS

So dx/dt=2.67×10^(-7)y-10.67x, where y=(1-exp(-2.67×10^(-7)t)(2.51×10^6), is that correct? Or dx/dt=2.67×10^(-7)y-1,067×10^(-6)x? Yes I have done integrating factors. I have no problem solving these equations only setting up the problem.

Thanks for answer but how do I represent the amount of pollutant in the second lake as a differential equation? I understood the process in Example 4 but not with the information of both lakes in problem 15.

The problem I'm stuck is 15. I added Example 4 so you can see what problem 15 is all about. What I've been trying is: the amount of pollutant in the first lake is y=(1-e^(-2.67*10^(-7)t)(2.51*10^6). So I multiplied y by the rate entering the second lake which is the one leaving the first lake. Then I multiply 10.67 by the amount of pollutant in the second lake which is what I have to find through a linear first-order differential equation. Then I have dc/dt=10.67y+10.67c. Something's wrong but I don't know what. I do not need help solving this kind of differential equations where I need help is FINDING THE DIFFERENTIAL EQUATION TO SOLVE.