I know its a long problem but I would appreciate the help!
2. We now use separation of variables to solve the above IVP. Use the hints and suggestions below. You may also want to refer to Example 4 from the lecture notes of Monday, Week 14. Please show all your work in the solutions that you turn in (i) Separate variables in the DE in (DM), and then take integrals on both sides, to show that dK where C is some constant. We haven't yet evaluated the integral on the left, but we will now (ii) Substitute u =ã-K into the above integral on the left. What is du, under this substitution? (Remember thatãhere is constant; the variable of integration is K.) Do the resulting integral in u, and then plug back in for u in terms of K, to conclude, from exercise (2) (i) above, that (iii Explain, in terms of the "real-world" implications of our setup here, why you can remove the above absolute value signs, to conclude that Hint: by assumption (B) above,ãis initially larger than K. The internal concen- tration K wl steadily increase, getting closer and closer to the external concen trationã. But there's no reason for the former to ever exceed the latter. So what does this tell us about the sign ofã-K?