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

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