I would expect an example matching an exercise in a text to be in the preceding chapter, not the "chapter to follow"!

Of course, you don't even say what type course this is so I have no idea what methods you might have available. But here is howIwould do it:

Let X(t) be the total amount of salt. in oz, in the tank at time t, on minutes. Then is the rate at which salt is coming into the the tank. We are told " oz of salt per gallon come into the tank at 2 gallons per minute" so oz of salt come into the tank every minute. With X oz of salt in a 201 gal tank, there are oz of salt in each gallon so if the mixture goes out at 2 gallons per minute, there are oz of salt leaving every minute.

That is, we have the equation . That is equivalent to the first order linear differential equation . (Is this a differential equations class?) The associated "homogeneous equation" is and its general solution is . That obviously will go to 0 very quickly and is called the "transient solution" by engineers. To find the "particular solution", the one that "lasts" (and is called the "steady state solution") look for a solution of the form . The " " is the "oscillation" of course, and is not relevant to the first part of this exercise which asks for the "constant level" the solution oscillates about and that is the number "A".

So- if you let X(t)= A, a constant, what value of A satisfies the differential equation? Obviously, and the " " is the " " part of the equation. Finding the "constant level the solution oscillates about" reduces to solving !

To find the amplitude of the oscillation means finding the amplitude of the function Bsin(t)+ Ccos(t) and that, of course, depends on B and C. Substitute X= B sin(t)+ C cos(t) into to determine what B and C must be.