dy/dx + P(x) y = Q(x). Show that y(x) = ye(x) + yp(x)

is a general solution of dy/dx + P(x) y = Q(x).

32. (a) Find constants A and B such that y, (x) = A sin x +

B cos x is a solution of dy/dx + y = 2 sinx. (b) Use the

result of part (a) and the method of Problem 31 to find the

general solution of dy/dx + y = 2 sinx. (c) Solve the

initial value problem dy/dx + y = 2 sinx, y(0) = 1.

33. A tank contains 1000 liters (L) of a solution consisting of

100 kg of salt dissolved in water. Pure water is pumped

into the tank at the rate of 5 L/s, and the mixture-kept

uniform by stirring— is pumped out at the same rate. How

long will it be until only 10 kg of salt remains in the tank?

34. Consider a reservoir with a volume of 8 billion cubic feet

(ft³) and an initial pollutant concentration of 0.25%. There

is a daily inflow of 500 million ft³ of water with a pollu-

tant concentration of 0.05% and an equal daily outflow of

the well-mixed water in the reservoir How long will it